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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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III","\u002Fzh\u002Fmicroeconomics\u002F00-intro","zh\u002Fmicroeconomics\u002F00-intro\u002Findex",[1552],{"title":1548,"path":1549,"stem":1550},{"title":1554,"path":1555,"stem":1556,"children":1557},"消费者理论与分析基础","\u002Fzh\u002Fmicroeconomics\u002F01-fundations","zh\u002Fmicroeconomics\u002F01-fundations\u002Findex",[1558],{"title":1554,"path":1555,"stem":1556},{"title":1560,"path":1561,"stem":1562,"children":1563},"比较静态分析与福利测度","\u002Fzh\u002Fmicroeconomics\u002F02-comparative-statics","zh\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[1564],{"title":1560,"path":1561,"stem":1562},{"title":1566,"path":1567,"stem":1568,"children":1569},"不确定性下的决策","\u002Fzh\u002Fmicroeconomics\u002F03-uncertainty","zh\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[1570],{"title":1566,"path":1567,"stem":1568},{"title":1572,"path":1573,"stem":1574,"children":1575},"一般均衡与福利经济学","\u002Fzh\u002Fmicroeconomics\u002F04-general-equilibrium","zh\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[1576],{"title":1572,"path":1573,"stem":1574},{"title":1578,"path":1579,"stem":1580,"children":1581},"博弈论：静态与动态博弈","\u002Fzh\u002Fmicroeconomics\u002F05-game-theory","zh\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[1582],{"title":1578,"path":1579,"stem":1580},{"title":1584,"path":1585,"stem":1586,"children":1587},"寡头垄断与策略性市场行为","\u002Fzh\u002Fmicroeconomics\u002F06-oligopoly","zh\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[1588],{"title":1584,"path":1585,"stem":1586},{"title":1590,"path":1591,"stem":1592,"children":1593},"信息经济学：逆向选择与道德风险","\u002Fzh\u002Fmicroeconomics\u002F07-information-economics","zh\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[1594],{"title":1590,"path":1591,"stem":1592},{"title":1596,"path":1597,"stem":1598,"children":1599},"机制设计与拍卖理论","\u002Fzh\u002Fmicroeconomics\u002F08-mechanism-design","zh\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[1600],{"title":1596,"path":1597,"stem":1598},{"title":1602,"path":1603,"stem":1604,"children":1605},"行为与实验微观经济学","\u002Fzh\u002Fmicroeconomics\u002F09-behavioural-economics","zh\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[1606],{"title":1602,"path":1603,"stem":1604},{"title":1608,"path":1609,"stem":1610,"children":1611},"外部性、公共物品与机制","\u002Fzh\u002Fmicroeconomics\u002F10-externalities-public-goods","zh\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[1612],{"title":1608,"path":1609,"stem":1610},{"title":1614,"path":1615,"stem":1616,"children":1617},"市场设计与匹配理论","\u002Fzh\u002Fmicroeconomics\u002F11-market-design","zh\u002Fmicroeconomics\u002F11-market-design\u002Findex",[1618],{"title":1614,"path":1615,"stem":1616},{"title":1620,"path":1621,"stem":1622,"children":1623},"第十二章：微观经济学：回顾与前沿应用","\u002Fzh\u002Fmicroeconomics\u002F12-review","zh\u002Fmicroeconomics\u002F12-review\u002Findex",[1624],{"title":1620,"path":1621,"stem":1622},{"title":799,"path":1626,"stem":1627,"children":1628,"page":249},"\u002Fzh\u002Fplayground","zh\u002Fplayground",[1629],{"title":1630,"path":1631,"stem":1632},"Chart.js 可视化","\u002Fzh\u002Fplayground\u002F05-chartjs","zh\u002Fplayground\u002F05-chartjs",{"title":1634,"path":1635,"stem":1636,"children":1637},"概率论与数理统计","\u002Fzh\u002Fprob-and-stats","zh\u002Fprob-and-stats\u002Findex",[1638,1639,1645,1680,1727],{"title":1634,"path":1635,"stem":1636},{"title":1640,"path":1641,"stem":1642,"children":1643},"第零章：概率统计的对象与学习方法","\u002Fzh\u002Fprob-and-stats\u002F00-intro","zh\u002Fprob-and-stats\u002F00-intro\u002Findex",[1644],{"title":1640,"path":1641,"stem":1642},{"title":1646,"path":1647,"stem":1648,"children":1649,"page":249},"01 Probability","\u002Fzh\u002Fprob-and-stats\u002F01-probability","zh\u002Fprob-and-stats\u002F01-probability",[1650,1656,1662,1668,1674],{"title":1651,"path":1652,"stem":1653,"children":1654},"第一章：概率论基础","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory","zh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory\u002Findex",[1655],{"title":1651,"path":1652,"stem":1653},{"title":1657,"path":1658,"stem":1659,"children":1660},"第二章：随机变量与分布","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables","zh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables\u002Findex",[1661],{"title":1657,"path":1658,"stem":1659},{"title":1663,"path":1664,"stem":1665,"children":1666},"第三章：期望、方差与条件矩","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F03-moment","zh\u002Fprob-and-stats\u002F01-probability\u002F03-moment\u002Findex",[1667],{"title":1663,"path":1664,"stem":1665},{"title":1669,"path":1670,"stem":1671,"children":1672},"第四章：常见分布族与建模机制","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F04-families","zh\u002Fprob-and-stats\u002F01-probability\u002F04-families\u002Findex",[1673],{"title":1669,"path":1670,"stem":1671},{"title":1675,"path":1676,"stem":1677,"children":1678},"第五章：收敛与渐近理论","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics","zh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics\u002Findex",[1679],{"title":1675,"path":1676,"stem":1677},{"title":1681,"path":1682,"stem":1683,"children":1684,"page":249},"02 Statistics","\u002Fzh\u002Fprob-and-stats\u002F02-statistics","zh\u002Fprob-and-stats\u002F02-statistics",[1685,1691,1697,1703,1709,1715,1721],{"title":1686,"path":1687,"stem":1688,"children":1689},"第六章：抽样分布","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling","zh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling\u002Findex",[1690],{"title":1686,"path":1687,"stem":1688},{"title":1692,"path":1693,"stem":1694,"children":1695},"第七章：区间估计","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation\u002Findex",[1696],{"title":1692,"path":1693,"stem":1694},{"title":1698,"path":1699,"stem":1700,"children":1701},"第八章：点估计理论","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation\u002Findex",[1702],{"title":1698,"path":1699,"stem":1700},{"title":1704,"path":1705,"stem":1706,"children":1707},"第九章：点估计方法","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method\u002Findex",[1708],{"title":1704,"path":1705,"stem":1706},{"title":1710,"path":1711,"stem":1712,"children":1713},"第十章：假设检验原理","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis","zh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis\u002Findex",[1714],{"title":1710,"path":1711,"stem":1712},{"title":1716,"path":1717,"stem":1718,"children":1719},"第十一章：常用检验方法与选择","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method\u002Findex",[1720],{"title":1716,"path":1717,"stem":1718},{"title":1722,"path":1723,"stem":1724,"children":1725},"第十二章：Bootstrap 与重抽样","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F07-bootstrap","zh\u002Fprob-and-stats\u002F02-statistics\u002F07-bootstrap\u002Findex",[1726],{"title":1722,"path":1723,"stem":1724},{"title":1728,"path":1729,"stem":1730},"第十三章：前沿文献与现代统计案例（2023—2026）","\u002Fzh\u002Fprob-and-stats\u002F03-frontier-literature-2026","zh\u002Fprob-and-stats\u002F03-frontier-literature-2026",{"title":1732,"path":1733,"stem":1734,"children":1735,"page":249},"Quant","\u002Fzh\u002Fquant","zh\u002Fquant",[1736,1742,1746,1750,1754,1758,1762,1766,1770,1774,1778],{"title":1737,"path":1738,"stem":1739,"children":1740},"量化投资——从可检验信号到可执行组合","\u002Fzh\u002Fquant\u002F00-index","zh\u002Fquant\u002F00-index",[1741],{"title":1737,"path":1738,"stem":1739},{"title":1743,"path":1744,"stem":1745},"数据获取与预处理","\u002Fzh\u002Fquant\u002F01-research-data","zh\u002Fquant\u002F01-research-data",{"title":1747,"path":1748,"stem":1749},"因子与交易信号","\u002Fzh\u002Fquant\u002F02-factor-and-signals","zh\u002Fquant\u002F02-factor-and-signals",{"title":1751,"path":1752,"stem":1753},"策略建模与回测","\u002Fzh\u002Fquant\u002F03-modeling-and-backtest","zh\u002Fquant\u002F03-modeling-and-backtest",{"title":1755,"path":1756,"stem":1757},"组合构建与风险建模（资产定价视角）","\u002Fzh\u002Fquant\u002F04-portfolio-and-risk","zh\u002Fquant\u002F04-portfolio-and-risk",{"title":1759,"path":1760,"stem":1761},"执行策略与市场微结构概览","\u002Fzh\u002Fquant\u002F05-execution-and-microstructure","zh\u002Fquant\u002F05-execution-and-microstructure",{"title":1763,"path":1764,"stem":1765},"策略上线、监控与迭代","\u002Fzh\u002Fquant\u002F06-production-and-monitoring","zh\u002Fquant\u002F06-production-and-monitoring",{"title":1767,"path":1768,"stem":1769},"量化工程与工具链概览","\u002Fzh\u002Fquant\u002F07-engineering-stack","zh\u002Fquant\u002F07-engineering-stack",{"title":1771,"path":1772,"stem":1773},"计量方法与实证检验","\u002Fzh\u002Fquant\u002F08-econometric-methods","zh\u002Fquant\u002F08-econometric-methods",{"title":1775,"path":1776,"stem":1777},"案例研究：多因子股票 Alpha 策略全流程","\u002Fzh\u002Fquant\u002F09-case-study","zh\u002Fquant\u002F09-case-study",{"title":1779,"path":1780,"stem":1781},"量化投资文献与软件图谱","\u002Fzh\u002Fquant\u002F10-reading-software-map","zh\u002Fquant\u002F10-reading-software-map",null,{"id":1784,"title":1692,"body":1785,"description":12830,"extension":12831,"features":1782,"hero":1782,"layout":1782,"locale":1782,"meta":12832,"navigation":1782,"path":1693,"published":12835,"seo":12836,"stem":1694,"__hash__":12837},"docs\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation\u002Findex.md",{"type":1786,"value":1787,"toc":12799},"minimark",[1788,1792,1796,1815,1819,1822,1846,1850,2115,2244,2247,2433,2489,2492,2573,2576,2581,2585,2592,2764,2796,2801,3060,3374,3377,3931,3934,3938,4001,4311,4314,4896,4928,4932,4939,4944,4947,4951,5156,5453,5456,5961,6084,6087,6091,6095,6098,6734,6767,6771,7021,7025,7028,8036,8039,8043,8046,8455,8511,8630,8935,9503,9506,9509,9619,9624,9628,9689,9693,9696,9972,10103,10354,10403,10797,10900,10904,10952,11188,11191,11194,11198,11201,11760,11764,11767,11772,11776,11779,11783,11786,11806,11838,12092,12148,12388,12391,12395,12398,12539,12542,12545,12568,12571,12588,12591,12752,12755,12788],[1789,1790,1692],"h1",{"id":1791},"第七章区间估计",[1793,1794,1795],"p",{},"点估计给出一个数，区间估计进一步说明这个数有多不确定。一个合格的置信区间必须回答：",[1797,1798,1799,1803,1806,1809,1812],"ol",{},[1800,1801,1802],"li",{},"区间针对哪个参数？",[1800,1804,1805],{},"覆盖概率来自什么重复抽样机制？",[1800,1807,1808],{},"公式是有限样本精确结果，还是大样本近似？",[1800,1810,1811],{},"方法依赖正态、独立同分布、方差齐性或其他条件吗？",[1800,1813,1814],{},"样本量很小、参数接近边界或分布偏斜时会怎样？",[1816,1817,1818],"h2",{"id":1818},"学习成果",[1793,1820,1821],{},"完成本章后，你应能够：",[1823,1824,1825,1828,1831,1834,1837,1840,1843],"ul",{},[1800,1826,1827],{},"正确解释置信水平与覆盖率，而不把参数误说成随机变量；",[1800,1829,1830],{},"从枢轴量推导正态均值、方差和均值差的精确区间；",[1800,1832,1833],{},"区分 z 区间、t 区间、Wald 区间和 Wilson 区间；",[1800,1835,1836],{},"使用渐近正态性和 Delta 方法构造一般参数区间；",[1800,1838,1839],{},"解释似然比区间、Bootstrap 区间和贝叶斯可信区间的差异；",[1800,1841,1842],{},"用 Python 与 R 做 Monte Carlo 覆盖率实验；",[1800,1844,1845],{},"根据参数边界、偏斜、样本量和数据依赖结构选择方法。",[1816,1847,1849],{"id":1848},"_1-置信区间究竟保证什么","1. 置信区间究竟保证什么",[1793,1851,1852,1853,2081,2082,2114],{},"设数据 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来自参数为 ",[1854,2083,2085,2100],{"className":2084},[1857],[1854,2086,2088],{"className":2087},[1861],[1863,2089,2090],{"xmlns":1865},[1867,2091,2092,2097],{},[1870,2093,2094],{},[1873,2095,2096],{},"θ",[1913,2098,2099],{"encoding":1915},"\\theta",[1854,2101,2103],{"className":2102,"ariaHidden":1895},[1920],[1854,2104,2106,2110],{"className":2105},[1924],[1854,2107],{"className":2108,"style":2109},[1928],"height:0.6944em;",[1854,2111,2096],{"className":2112,"style":2113},[1933,1934],"margin-right:0.0278em;"," 的模型。区间",[1854,2116,2119],{"className":2117},[2118],"katex-display",[1854,2120,2122,2172],{"className":2121},[1857],[1854,2123,2125],{"className":2124},[1861],[1863,2126,2128],{"xmlns":1865,"display":2127},"block",[1867,2129,2130,2169],{},[1870,2131,2132,2135,2137,2139,2141,2143,2146,2149,2151,2153,2155,2157,2160,2162,2164,2166],{},[1873,2133,2134],{},"C",[1877,2136,1883],{"stretchy":1882},[1873,2138,1875],{},[1877,2140,1911],{"stretchy":1882},[1877,2142,1879],{},[1877,2144,2145],{"stretchy":1882},"[",[1873,2147,2148],{},"L",[1877,2150,1883],{"stretchy":1882},[1873,2152,1875],{},[1877,2154,1911],{"stretchy":1882},[1877,2156,1896],{"separator":1895},[1873,2158,2159],{},"U",[1877,2161,1883],{"stretchy":1882},[1873,2163,1875],{},[1877,2165,1911],{"stretchy":1882},[1877,2167,2168],{"stretchy":1882},"]",[1913,2170,2171],{"encoding":1915},"C(X)=[L(X),U(X)]",[1854,2173,2175,2203],{"className":2174,"ariaHidden":1895},[1920],[1854,2176,2178,2181,2185,2188,2191,2194,2197,2200],{"className":2177},[1924],[1854,2179],{"className":2180,"style":1954},[1928],[1854,2182,2134],{"className":2183,"style":2184},[1933,1934],"margin-right:0.0715em;",[1854,2186,1883],{"className":2187},[1958],[1854,2189,1875],{"className":2190,"style":1935},[1933,1934],[1854,2192,1911],{"className":2193},[2080],[1854,2195],{"className":2196,"style":1940},[1939],[1854,2198,1879],{"className":2199},[1944],[1854,2201],{"className":2202,"style":1940},[1939],[1854,2204,2206,2209,2212,2215,2218,2221,2224,2227,2230,2234,2237,2240],{"className":2205},[1924],[1854,2207],{"className":2208,"style":1954},[1928],[1854,2210,2145],{"className":2211},[1958],[1854,2213,2148],{"className":2214},[1933,1934],[1854,2216,1883],{"className":2217},[1958],[1854,2219,1875],{"className":2220,"style":1935},[1933,1934],[1854,2222,1911],{"className":2223},[2080],[1854,2225,1896],{"className":2226},[2018],[1854,2228],{"className":2229,"style":2022},[1939],[1854,2231,2159],{"className":2232,"style":2233},[1933,1934],"margin-right:0.109em;",[1854,2235,1883],{"className":2236},[1958],[1854,2238,1875],{"className":2239,"style":1935},[1933,1934],[1854,2241,2243],{"className":2242},[2080],")]",[1793,2245,2246],{},"是样本的函数，因此重复抽样时会变化。若",[1854,2248,2250],{"className":2249},[2118],[1854,2251,2253,2303],{"className":2252},[1857],[1854,2254,2256],{"className":2255},[1861],[1863,2257,2258],{"xmlns":1865,"display":2127},[1867,2259,2260,2300],{},[1870,2261,2262,2269,2272,2274,2277,2279,2281,2283,2285,2288,2290,2292,2295,2298],{},[1885,2263,2264,2267],{},[1873,2265,2266],{},"P",[1873,2268,2096],{},[1877,2270,2271],{"stretchy":1882},"{",[1873,2273,2096],{},[1877,2275,2276],{},"∈",[1873,2278,2134],{},[1877,2280,1883],{"stretchy":1882},[1873,2282,1875],{},[1877,2284,1911],{"stretchy":1882},[1877,2286,2287],{"stretchy":1882},"}",[1877,2289,1879],{},[1890,2291,1892],{},[1877,2293,2294],{},"−",[1873,2296,2297],{},"α",[1877,2299,1896],{"separator":1895},[1913,2301,2302],{"encoding":1915},"P_\\theta\\{\\theta\\in C(X)\\}=1-\\alpha,",[1854,2304,2306,2370,2398,2419],{"className":2305,"ariaHidden":1895},[1920],[1854,2307,2309,2312,2355,2358,2361,2364,2367],{"className":2308},[1924],[1854,2310],{"className":2311,"style":1954},[1928],[1854,2313,2315,2319],{"className":2314},[1933],[1854,2316,2266],{"className":2317,"style":2318},[1933,1934],"margin-right:0.1389em;",[1854,2320,2322],{"className":2321},[1968],[1854,2323,2325,2347],{"className":2324},[1972,1973],[1854,2326,2328,2344],{"className":2327},[1977],[1854,2329,2332],{"className":2330,"style":2331},[1981],"height:0.3361em;",[1854,2333,2335,2338],{"style":2334},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1854,2336],{"className":2337,"style":1990},[1989],[1854,2339,2341],{"className":2340},[1994,1995,1996,1997],[1854,2342,2096],{"className":2343,"style":2113},[1933,1934,1997],[1854,2345,2005],{"className":2346},[2004],[1854,2348,2350],{"className":2349},[1977],[1854,2351,2353],{"className":2352,"style":2012},[1981],[1854,2354],{},[1854,2356,2271],{"className":2357},[1958],[1854,2359,2096],{"className":2360,"style":2113},[1933,1934],[1854,2362],{"className":2363,"style":1940},[1939],[1854,2365,2276],{"className":2366},[1944],[1854,2368],{"className":2369,"style":1940},[1939],[1854,2371,2373,2376,2379,2382,2385,2389,2392,2395],{"className":2372},[1924],[1854,2374],{"className":2375,"style":1954},[1928],[1854,2377,2134],{"className":2378,"style":2184},[1933,1934],[1854,2380,1883],{"className":2381},[1958],[1854,2383,1875],{"className":2384,"style":1935},[1933,1934],[1854,2386,2388],{"className":2387},[2080],")}",[1854,2390],{"className":2391,"style":1940},[1939],[1854,2393,1879],{"className":2394},[1944],[1854,2396],{"className":2397,"style":1940},[1939],[1854,2399,2401,2405,2408,2412,2416],{"className":2400},[1924],[1854,2402],{"className":2403,"style":2404},[1928],"height:0.7278em;vertical-align:-0.0833em;",[1854,2406,1892],{"className":2407},[1933],[1854,2409],{"className":2410,"style":2411},[1939],"margin-right:0.2222em;",[1854,2413,2294],{"className":2414},[2415],"mbin",[1854,2417],{"className":2418,"style":2411},[1939],[1854,2420,2422,2426,2430],{"className":2421},[1924],[1854,2423],{"className":2424,"style":2425},[1928],"height:0.625em;vertical-align:-0.1944em;",[1854,2427,2297],{"className":2428,"style":2429},[1933,1934],"margin-right:0.0037em;",[1854,2431,1896],{"className":2432},[2018],[1793,2434,2435,2436,2488],{},"则称它是覆盖率为 ",[1854,2437,2439,2457],{"className":2438},[1857],[1854,2440,2442],{"className":2441},[1861],[1863,2443,2444],{"xmlns":1865},[1867,2445,2446,2454],{},[1870,2447,2448,2450,2452],{},[1890,2449,1892],{},[1877,2451,2294],{},[1873,2453,2297],{},[1913,2455,2456],{"encoding":1915},"1-\\alpha",[1854,2458,2460,2478],{"className":2459,"ariaHidden":1895},[1920],[1854,2461,2463,2466,2469,2472,2475],{"className":2462},[1924],[1854,2464],{"className":2465,"style":2404},[1928],[1854,2467,1892],{"className":2468},[1933],[1854,2470],{"className":2471,"style":2411},[1939],[1854,2473,2294],{"className":2474},[2415],[1854,2476],{"className":2477,"style":2411},[1939],[1854,2479,2481,2485],{"className":2480},[1924],[1854,2482],{"className":2483,"style":2484},[1928],"height:0.4306em;",[1854,2486,2297],{"className":2487,"style":2429},[1933,1934]," 的置信区间。",[1793,2490,2491],{},"频率学派的正确解释是：",[2493,2494,2495],"blockquote",{},[1793,2496,2497,2498,2572],{},"若按同一抽样设计无限次重复收集数据并构造区间，长期约有 ",[1854,2499,2501,2530],{"className":2500},[1857],[1854,2502,2504],{"className":2503},[1861],[1863,2505,2506],{"xmlns":1865},[1867,2507,2508,2527],{},[1870,2509,2510,2513,2515,2517,2519,2521,2523],{},[1890,2511,2512],{},"100",[1877,2514,1883],{"stretchy":1882},[1890,2516,1892],{},[1877,2518,2294],{},[1873,2520,2297],{},[1877,2522,1911],{"stretchy":1882},[1873,2524,2526],{"mathvariant":2525},"normal","%",[1913,2528,2529],{"encoding":1915},"100(1-\\alpha)\\%",[1854,2531,2533,2557],{"className":2532,"ariaHidden":1895},[1920],[1854,2534,2536,2539,2542,2545,2548,2551,2554],{"className":2535},[1924],[1854,2537],{"className":2538,"style":1954},[1928],[1854,2540,2512],{"className":2541},[1933],[1854,2543,1883],{"className":2544},[1958],[1854,2546,1892],{"className":2547},[1933],[1854,2549],{"className":2550,"style":2411},[1939],[1854,2552,2294],{"className":2553},[2415],[1854,2555],{"className":2556,"style":2411},[1939],[1854,2558,2560,2563,2566,2569],{"className":2559},[1924],[1854,2561],{"className":2562,"style":1954},[1928],[1854,2564,2297],{"className":2565,"style":2429},[1933,1934],[1854,2567,1911],{"className":2568},[2080],[1854,2570,2526],{"className":2571},[1933]," 的区间覆盖固定真参数。",[1793,2574,2575],{},"观测到具体区间后，它要么覆盖真参数，要么没有覆盖。不能在不引入贝叶斯后验的情况下说“这个固定参数有 95% 概率落在已经算出的区间内”。",[2577,2578,2580],"warning",{"title":2579},"置信水平不是研究结论为真的概率","95% 置信区间描述构造程序的长期覆盖性质。它不表示模型有 95% 概率正确，也不表示重复研究有 95% 概率显著。",[1816,2582,2584],{"id":2583},"_2-枢轴量精确区间的核心","2. 枢轴量：精确区间的核心",[1793,2586,2587,2591],{},[2588,2589,2590],"strong",{},"枢轴量","是同时依赖样本和未知参数，但其分布不依赖未知参数的统计量。若",[1854,2593,2595],{"className":2594},[2118],[1854,2596,2598,2650],{"className":2597},[1857],[1854,2599,2601],{"className":2600},[1861],[1863,2602,2603],{"xmlns":1865,"display":2127},[1867,2604,2605,2647],{},[1870,2606,2607,2609,2611,2614,2617,2620,2622,2624,2626,2628,2630,2632,2635,2637,2639,2641,2643,2645],{},[1873,2608,2266],{},[1877,2610,2271],{"stretchy":1882},[1873,2612,2613],{},"a",[1877,2615,2616],{},"≤",[1873,2618,2619],{},"Q",[1877,2621,1883],{"stretchy":1882},[1873,2623,1875],{},[1877,2625,1896],{"separator":1895},[1873,2627,2096],{},[1877,2629,1911],{"stretchy":1882},[1877,2631,2616],{},[1873,2633,2634],{},"b",[1877,2636,2287],{"stretchy":1882},[1877,2638,1879],{},[1890,2640,1892],{},[1877,2642,2294],{},[1873,2644,2297],{},[1877,2646,1896],{"separator":1895},[1913,2648,2649],{"encoding":1915},"P\\{a\\le Q(X,\\theta)\\le 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已知，则",[1854,3061,3063],{"className":3062},[2118],[1854,3064,3066,3129],{"className":3065},[1857],[1854,3067,3069],{"className":3068},[1861],[1863,3070,3071],{"xmlns":1865,"display":2127},[1867,3072,3073,3126],{},[1870,3074,3075,3078,3080,3108,3110,3112,3114,3117,3119,3121,3123],{},[1873,3076,3077],{},"Z",[1877,3079,1879],{},[3081,3082,3083,3096],"mfrac",{},[1870,3084,3085,3092,3094],{},[2826,3086,3087,3089],{"accent":1895},[1873,3088,1875],{},[1877,3090,3091],{},"ˉ",[1877,3093,2294],{},[1873,3095,2849],{},[1870,3097,3098,3100,3103],{},[1873,3099,2857],{},[1873,3101,3102],{"mathvariant":2525},"\u002F",[3104,3105,3106],"msqrt",{},[1873,3107,1908],{},[1877,3109,2832],{},[1873,3111,2844],{},[1877,3113,1883],{"stretchy":1882},[1890,3115,3116],{},"0",[1877,3118,1896],{"separator":1895},[1890,3120,1892],{},[1877,3122,1911],{"stretchy":1882},[1873,3124,3125],{"mathvariant":2525},".",[1913,3127,3128],{"encoding":1915},"Z=\\frac{\\bar X-\\mu}{\\sigma\u002F\\sqrt n}\\sim 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X-z_{1-\\alpha\u002F2}\\frac{\\sigma}{\\sqrt n},\n\\bar X+z_{1-\\alpha\u002F2}\\frac{\\sigma}{\\sqrt n}\n\\right].",[1854,3476,3478,3497],{"className":3477,"ariaHidden":1895},[1920],[1854,3479,3481,3485,3488,3491,3494],{"className":3480},[1924],[1854,3482],{"className":3483,"style":3484},[1928],"height:0.7335em;vertical-align:-0.1944em;",[1854,3486,2849],{"className":3487},[1933,1934],[1854,3489],{"className":3490,"style":1940},[1939],[1854,3492,2276],{"className":3493},[1944],[1854,3495],{"className":3496,"style":1940},[1939],[1854,3498,3500,3504,3925,3928],{"className":3499},[1924],[1854,3501],{"className":3502,"style":3503},[1928],"height:2.4em;vertical-align:-0.95em;",[1854,3505,3507,3516,3547,3550,3553,3556,3613,3718,3721,3724,3755,3758,3761,3764,3816,3919],{"className":3506},[2026],[1854,3508,3512],{"className":3509,"style":3511},[1958,3510],"delimcenter","top:0em;",[1854,3513,2145],{"className":3514},[3515,1996],"delimsizing",[1854,3517,3519],{"className":3518},[1933,3275],[1854,3520,3522],{"className":3521},[1972],[1854,3523,3525],{"className":3524},[1977],[1854,3526,3528,3536],{"className":3527,"style":3285},[1981],[1854,3529,3530,3533],{"style":2940},[1854,3531],{"className":3532,"style":2944},[1989],[1854,3534,1875],{"className":3535,"style":1935},[1933,1934],[1854,3537,3538,3541],{"style":3296},[1854,3539],{"className":3540,"style":2944},[1989],[1854,3542,3544],{"className":3543,"style":3304},[3303],[1854,3545,3091],{"className":3546},[1933],[1854,3548],{"className":3549,"style":2411},[1939],[1854,3551,2294],{"className":3552},[2415],[1854,3554],{"className":3555,"style":2411},[1939],[1854,3557,3559,3563],{"className":3558},[1933],[1854,3560,3412],{"className":3561,"style":3562},[1933,1934],"margin-right:0.044em;",[1854,3564,3566],{"className":3565},[1968],[1854,3567,3569,3604],{"className":3568},[1972,1973],[1854,3570,3572,3601],{"className":3571},[1977],[1854,3573,3576],{"className":3574,"style":3575},[1981],"height:0.3448em;",[1854,3577,3579,3582],{"style":3578},"top:-2.5198em;margin-left:-0.044em;margin-right:0.05em;",[1854,3580],{"className":3581,"style":1990},[1989],[1854,3583,3585],{"className":3584},[1994,1995,1996,1997],[1854,3586,3588,3591,3594,3597],{"className":3587},[1933,1997],[1854,3589,1892],{"className":3590},[1933,1997],[1854,3592,2294],{"className":3593},[2415,1997],[1854,3595,2297],{"className":3596,"style":2429},[1933,1934,1997],[1854,3598,3600],{"className":3599},[1933,1997],"\u002F2",[1854,3602,2005],{"className":3603},[2004],[1854,3605,3607],{"className":3606},[1977],[1854,3608,3611],{"className":3609,"style":3610},[1981],"height:0.3552em;",[1854,3612],{},[1854,3614,3616,3619,3715],{"className":3615},[1933],[1854,3617],{"className":3618},[1958,3163],[1854,3620,3622],{"className":3621},[3081],[1854,3623,3625,3706],{"className":3624},[1972,1973],[1854,3626,3628,3703],{"className":3627},[1977],[1854,3629,3632,3684,3692],{"className":3630,"style":3631},[1981],"height:1.1076em;",[1854,3633,3634,3637],{"style":3179},[1854,3635],{"className":3636,"style":2944},[1989],[1854,3638,3640],{"className":3639},[1933],[1854,3641,3643],{"className":3642},[1933,3195],[1854,3644,3646,3676],{"className":3645},[1972,1973],[1854,3647,3649,3673],{"className":3648},[1977],[1854,3650,3652,3661],{"className":3651,"style":3205},[1981],[1854,3653,3655,3658],{"className":3654,"style":2940},[3209],[1854,3656],{"className":3657,"style":2944},[1989],[1854,3659,1908],{"className":3660,"style":3216},[1933,1934],[1854,3662,3663,3666],{"style":3219},[1854,3664],{"className":3665,"style":2944},[1989],[1854,3667,3669],{"className":3668,"style":3227},[3226],[3229,3670,3671],{"xmlns":3231,"width":3232,"height":3233,"viewBox":3234,"preserveAspectRatio":3235},[3237,3672],{"d":3239},[1854,3674,2005],{"className":3675},[2004],[1854,3677,3679],{"className":3678},[1977],[1854,3680,3682],{"className":3681,"style":3249},[1981],[1854,3683],{},[1854,3685,3686,3689],{"style":3254},[1854,3687],{"className":3688,"style":2944},[1989],[1854,3690],{"className":3691,"style":3262},[3261],[1854,3693,3694,3697],{"style":3265},[1854,3695],{"className":3696,"style":2944},[1989],[1854,3698,3700],{"className":3699},[1933],[1854,3701,2857],{"className":3702,"style":3000},[1933,1934],[1854,3704,2005],{"className":3705},[2004],[1854,3707,3709],{"className":3708},[1977],[1854,3710,3713],{"className":3711,"style":3712},[1981],"height:0.93em;",[1854,3714],{},[1854,3716],{"className":3717},[2080,3163],[1854,3719,1896],{"className":3720},[2018],[1854,3722],{"className":3723,"style":2022},[1939],[1854,3725,3727],{"className":3726},[1933,3275],[1854,3728,3730],{"className":3729},[1972],[1854,3731,3733],{"className":3732},[1977],[1854,3734,3736,3744],{"className":3735,"style":3285},[1981],[1854,3737,3738,3741],{"style":2940},[1854,3739],{"className":3740,"style":2944},[1989],[1854,3742,1875],{"className":3743,"style":1935},[1933,1934],[1854,3745,3746,3749],{"style":3296},[1854,3747],{"className":3748,"style":2944},[1989],[1854,3750,3752],{"className":3751,"style":3304},[3303],[1854,3753,3091],{"className":3754},[1933],[1854,3756],{"className":3757,"style":2411},[1939],[1854,3759,3443],{"className":3760},[2415],[1854,3762],{"className":3763,"style":2411},[1939],[1854,3765,3767,3770],{"className":3766},[1933],[1854,3768,3412],{"className":3769,"style":3562},[1933,1934],[1854,3771,3773],{"className":3772},[1968],[1854,3774,3776,3808],{"className":3775},[1972,1973],[1854,3777,3779,3805],{"className":3778},[1977],[1854,3780,3782],{"className":3781,"style":3575},[1981],[1854,3783,3784,3787],{"style":3578},[1854,3785],{"className":3786,"style":1990},[1989],[1854,3788,3790],{"className":3789},[1994,1995,1996,1997],[1854,3791,3793,3796,3799,3802],{"className":3792},[1933,1997],[1854,3794,1892],{"className":3795},[1933,1997],[1854,3797,2294],{"className":3798},[2415,1997],[1854,3800,2297],{"className":3801,"style":2429},[1933,1934,1997],[1854,3803,3600],{"className":3804},[1933,1997],[1854,3806,2005],{"className":3807},[2004],[1854,3809,3811],{"className":3810},[1977],[1854,3812,3814],{"className":3813,"style":3610},[1981],[1854,3815],{},[1854,3817,3819,3822,3916],{"className":3818},[1933],[1854,3820],{"className":3821},[1958,3163],[1854,3823,3825],{"className":3824},[3081],[1854,3826,3828,3908],{"className":3827},[1972,1973],[1854,3829,3831,3905],{"className":3830},[1977],[1854,3832,3834,3886,3894],{"className":3833,"style":3631},[1981],[1854,3835,3836,3839],{"style":3179},[1854,3837],{"className":3838,"style":2944},[1989],[1854,3840,3842],{"className":3841},[1933],[1854,3843,3845],{"className":3844},[1933,3195],[1854,3846,3848,3878],{"className":3847},[1972,1973],[1854,3849,3851,3875],{"className":3850},[1977],[1854,3852,3854,3863],{"className":3853,"style":3205},[1981],[1854,3855,3857,3860],{"className":3856,"style":2940},[3209],[1854,3858],{"className":3859,"style":2944},[1989],[1854,3861,1908],{"className":3862,"style":3216},[1933,1934],[1854,3864,3865,3868],{"style":3219},[1854,3866],{"className":3867,"style":2944},[1989],[1854,3869,3871],{"className":3870,"style":3227},[3226],[3229,3872,3873],{"xmlns":3231,"width":3232,"height":3233,"viewBox":3234,"preserveAspectRatio":3235},[3237,3874],{"d":3239},[1854,3876,2005],{"className":3877},[2004],[1854,3879,3881],{"className":3880},[1977],[1854,3882,3884],{"className":3883,"style":3249},[1981],[1854,3885],{},[1854,3887,3888,3891],{"style":3254},[1854,3889],{"className":3890,"style":2944},[1989],[1854,3892],{"className":3893,"style":3262},[3261],[1854,3895,3896,3899],{"style":3265},[1854,3897],{"className":3898,"style":2944},[1989],[1854,3900,3902],{"className":3901},[1933],[1854,3903,2857],{"className":3904,"style":3000},[1933,1934],[1854,3906,2005],{"className":3907},[2004],[1854,3909,3911],{"className":3910},[1977],[1854,3912,3914],{"className":3913,"style":3712},[1981],[1854,3915],{},[1854,3917],{"className":3918},[2080,3163],[1854,3920,3922],{"className":3921,"style":3511},[2080,3510],[1854,3923,2168],{"className":3924},[3515,1996],[1854,3926],{"className":3927,"style":2022},[1939],[1854,3929,3125],{"className":3930},[1933],[1793,3932,3933],{},"区间半宽由临界值、总体波动和样本量共同决定。样本量增加四倍，标准误和区间半宽约减半。",[2797,3935,3937],{"id":3936},"_22-正态均值方差未知","2.2 正态均值、方差未知",[1793,3939,3940,3941,3971,3972,4000],{},"用样本标准差 ",[1854,3942,3944,3958],{"className":3943},[1857],[1854,3945,3947],{"className":3946},[1861],[1863,3948,3949],{"xmlns":1865},[1867,3950,3951,3956],{},[1870,3952,3953],{},[1873,3954,3955],{},"S",[1913,3957,3955],{"encoding":1915},[1854,3959,3961],{"className":3960,"ariaHidden":1895},[1920],[1854,3962,3964,3967],{"className":3963},[1924],[1854,3965],{"className":3966,"style":1929},[1928],[1854,3968,3955],{"className":3969,"style":3970},[1933,1934],"margin-right:0.0576em;"," 替代未知 ",[1854,3973,3975,3988],{"className":3974},[1857],[1854,3976,3978],{"className":3977},[1861],[1863,3979,3980],{"xmlns":1865},[1867,3981,3982,3986],{},[1870,3983,3984],{},[1873,3985,2857],{},[1913,3987,3046],{"encoding":1915},[1854,3989,3991],{"className":3990,"ariaHidden":1895},[1920],[1854,3992,3994,3997],{"className":3993},[1924],[1854,3995],{"className":3996,"style":2484},[1928],[1854,3998,2857],{"className":3999,"style":3000},[1933,1934]," 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t_{n-1}.",[1854,4066,4068,4086,4250],{"className":4067,"ariaHidden":1895},[1920],[1854,4069,4071,4074,4077,4080,4083],{"className":4070},[1924],[1854,4072],{"className":4073,"style":1929},[1928],[1854,4075,4018],{"className":4076,"style":2318},[1933,1934],[1854,4078],{"className":4079,"style":1940},[1939],[1854,4081,1879],{"className":4082},[1944],[1854,4084],{"className":4085,"style":1940},[1939],[1854,4087,4089,4092,4241,4244,4247],{"className":4088},[1924],[1854,4090],{"className":4091,"style":3156},[1928],[1854,4093,4095,4098,4238],{"className":4094},[1933],[1854,4096],{"className":4097},[1958,3163],[1854,4099,4101],{"className":4100},[3081],[1854,4102,4104,4230],{"className":4103},[1972,1973],[1854,4105,4107,4227],{"className":4106},[1977],[1854,4108,4110,4168,4176],{"className":4109,"style":3176},[1981],[1854,4111,4112,4115],{"style":3179},[1854,4113],{"className":4114,"style":2944},[1989],[1854,4116,4118,4121,4124],{"className":4117},[1933],[1854,4119,3955],{"className":4120,"style":3970},[1933,1934],[1854,4122,3102],{"className":4123},[1933],[1854,4125,4127],{"className":4126},[1933,3195],[1854,4128,4130,4160],{"className":4129},[1972,1973],[1854,4131,4133,4157],{"className":4132},[1977],[1854,4134,4136,4145],{"className":4135,"style":3205},[1981],[1854,4137,4139,4142],{"className":4138,"style":2940},[3209],[1854,4140],{"className":4141,"style":2944},[1989],[1854,4143,1908],{"className":4144,"style":3216},[1933,1934],[1854,4146,4147,4150],{"style":3219},[1854,4148],{"className":4149,"style":2944},[1989],[1854,4151,4153],{"className":4152,"style":3227},[3226],[3229,4154,4155],{"xmlns":3231,"width":3232,"height":3233,"viewBox":3234,"preserveAspectRatio":3235},[3237,4156],{"d":3239},[1854,4158,2005],{"className":4159},[2004],[1854,4161,4163],{"className":4162},[1977],[1854,4164,4166],{"className":4165,"style":3249},[1981],[1854,4167],{},[1854,4169,4170,4173],{"style":3254},[1854,4171],{"className":4172,"style":2944},[1989],[1854,4174],{"className":4175,"style":3262},[3261],[1854,4177,4178,4181],{"style":3265},[1854,4179],{"className":4180,"style":2944},[1989],[1854,4182,4184,4215,4218,4221,4224],{"className":4183},[1933],[1854,4185,4187],{"className":4186},[1933,3275],[1854,4188,4190],{"className":4189},[1972],[1854,4191,4193],{"className":4192},[1977],[1854,4194,4196,4204],{"className":4195,"style":3285},[1981],[1854,4197,4198,4201],{"style":2940},[1854,4199],{"className":4200,"style":2944},[1989],[1854,4202,1875],{"className":4203,"style":1935},[1933,1934],[1854,4205,4206,4209],{"style":3296},[1854,4207],{"className":4208,"style":2944},[1989],[1854,4210,4212],{"className":4211,"style":3304},[3303],[1854,4213,3091],{"className":4214},[1933],[1854,4216],{"className":4217,"style":2411},[1939],[1854,4219,2294],{"className":4220},[2415],[1854,4222],{"className":4223,"style":2411},[1939],[1854,4225,2849],{"className":4226},[1933,1934],[1854,4228,2005],{"className":4229},[2004],[1854,4231,4233],{"className":4232},[1977],[1854,4234,4236],{"className":4235,"style":3329},[1981],[1854,4237],{},[1854,4239],{"className":4240},[2080,3163],[1854,4242],{"className":4243,"style":1940},[1939],[1854,4245,2832],{"className":4246},[1944],[1854,4248],{"className":4249,"style":1940},[1939],[1854,4251,4253,4257,4308],{"className":4252},[1924],[1854,4254],{"className":4255,"style":4256},[1928],"height:0.8234em;vertical-align:-0.2083em;",[1854,4258,4260,4263],{"className":4259},[1933],[1854,4261,4051],{"className":4262},[1933,1934],[1854,4264,4266],{"className":4265},[1968],[1854,4267,4269,4299],{"className":4268},[1972,1973],[1854,4270,4272,4296],{"className":4271},[1977],[1854,4273,4275],{"className":4274,"style":1982},[1981],[1854,4276,4278,4281],{"style":4277},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1854,4279],{"className":4280,"style":1990},[1989],[1854,4282,4284],{"className":4283},[1994,1995,1996,1997],[1854,4285,4287,4290,4293],{"className":4286},[1933,1997],[1854,4288,1908],{"className":4289},[1933,1934,1997],[1854,4291,2294],{"className":4292},[2415,1997],[1854,4294,1892],{"className":4295},[1933,1997],[1854,4297,2005],{"className":4298},[2004],[1854,4300,4302],{"className":4301},[1977],[1854,4303,4306],{"className":4304,"style":4305},[1981],"height:0.2083em;",[1854,4307],{},[1854,4309,3125],{"className":4310},[1933],[1793,4312,4313],{},"精确区间为：",[1854,4315,4317],{"className":4316},[2118],[1854,4318,4320,4426],{"className":4319},[1857],[1854,4321,4323],{"className":4322},[1861],[1863,4324,4325],{"xmlns":1865,"display":2127},[1867,4326,4327,4423],{},[1870,4328,4329,4331,4333,4421],{},[1873,4330,2849],{},[1877,4332,2276],{},[1870,4334,4335,4337,4343,4345,4369,4377,4379,4385,4387,4411,4419],{},[1877,4336,2145],{"fence":1895},[2826,4338,4339,4341],{"accent":1895},[1873,4340,1875],{},[1877,4342,3091],{},[1877,4344,2294],{},[1885,4346,4347,4349],{},[1873,4348,4051],{},[1870,4350,4351,4353,4355,4357,4359,4361,4363,4365,4367],{},[1890,4352,1892],{},[1877,4354,2294],{},[1873,4356,2297],{},[1873,4358,3102],{"mathva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临界值比 1.96 大，是因为估计 ",[1854,4900,4902,4915],{"className":4901},[1857],[1854,4903,4905],{"className":4904},[1861],[1863,4906,4907],{"xmlns":1865},[1867,4908,4909,4913],{},[1870,4910,4911],{},[1873,4912,2857],{},[1913,4914,3046],{"encoding":1915},[1854,4916,4918],{"className":4917,"ariaHidden":1895},[1920],[1854,4919,4921,4924],{"className":4920},[1924],[1854,4922],{"className":4923,"style":2484},[1928],[1854,4925,2857],{"className":4926,"style":3000},[1933,1934]," 引入额外不确定性。",[2797,4929,4931],{"id":4930},"交互例子一次小样本均值区间","交互例子：一次小样本均值区间",[4933,4934],"pyodide",{"code64":4935,"layout":4936,"locale":7,"packages":4937,"title":4938},"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","vertical","numpy, scipy","Python：手工构造 t 区间",[4940,4941],"web-r",{"code64":4942,"layout":4936,"locale":7,"title":4943},"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","R：手工构造 t 区间",[1793,4945,4946],{},"把置信水平改为 0.90 或 0.99，观察区间宽度。提高置信水平意味着要求构造程序更常覆盖真值，因此必须接受更宽区间。",[1816,4948,4950],{"id":4949},"_3-正态总体方差的精确区间","3. 正态总体方差的精确区间",[1793,4952,2803,4953,5155],{},[1854,4954,4956,5005],{"className":4955},[1857],[1854,4957,4959],{"className":4958},[1861],[1863,4960,4961],{"xmlns":1865},[1867,4962,4963,5003],{},[1870,4964,4965,4971,4987,4989,4991,4993,4995,5001],{},[1885,4966,4967,4969],{},[1873,4968,1875],{},[1873,4970,2822],{},[1877,4972,4973],{},[2826,4974,4975,4979],{},[1877,4976,4977],{},[1877,4978,2832],{},[1870,4980,4981,4983,4985],{},[1873,4982,2822],{},[1873,4984,2822],{},[1873,4986,2841],{},[1873,4988,2844],{},[1877,4990,1883],{"stretchy":1882},[1873,4992,2849],{},[1877,4994,1896],{"separator":1895},[2853,4996,4997,4999],{},[1873,4998,2857],{},[1890,5000,2860],{},[1877,5002,1911],{"stretchy":1882},[1913,5004,2865],{"encoding":1915},[1854,5006,5008,5102],{"className":5007,"ariaHidden":1895},[1920],[1854,5009,5011,5014,5054,5057,5099],{"className":5010},[1924],[1854,5012],{"className":5013,"style":2875},[1928],[1854,5015,5017,5020],{"className":5016},[1933],[1854,5018,1875],{"className":5019,"style":1935},[1933,1934],[1854,5021,5023],{"className":5022},[1968],[1854,5024,5026,5046],{"className":5025},[1972,1973],[1854,5027,5029,5043],{"className":5028},[1977],[1854,5030,5032],{"className":5031,"style":2894},[1981],[1854,5033,5034,5037],{"style":1985},[1854,5035],{"className":5036,"style":1990},[1989],[1854,5038,5040],{"className":5039},[1994,1995,1996,1997],[1854,5041,2822],{"className":5042},[1933,1934,1997],[1854,5044,2005],{"className":5045},[2004],[1854,5047,5049],{"className":5048},[1977],[1854,5050,5052],{"className":5051,"style":2012},[1981],[1854,5053],{},[1854,5055],{"className":5056,"style":1940},[1939],[1854,5058,5060],{"className":5059},[1944],[1854,5061,5063],{"className":5062},[2926,2927],[1854,5064,5066],{"className":5065},[1972],[1854,5067,5069],{"className":5068},[1977],[1854,5070,5072,5082],{"className":5071,"style":2937},[1981],[1854,5073,5074,5077],{"style":2940},[1854,5075],{"className":5076,"style":2944},[1989],[1854,5078,5079],{},[1854,5080,2832],{"className":5081},[2926],[1854,5083,5084,5087],{"style":2952},[1854,5085],{"className":5086,"style":2944},[1989],[1854,5088,5090],{"className":5089},[1994,1995,1996,1997],[1854,5091,5093,5096],{"className":5092},[1933,1997],[1854,5094,2965],{"className":5095},[1933,1934,1997],[1854,5097,2841],{"className":5098},[1933,1934,1997],[1854,5100],{"className":5101,"style":1940},[1939],[1854,5103,5105,5108,5111,5114,5117,5120,5123,5152],{"className":5104},[1924],[1854,5106],{"className":5107,"style":2978},[1928],[1854,5109,2844],{"className":5110,"style":2233},[1933,1934],[1854,5112,1883],{"className":5113},[1958],[1854,5115,2849],{"className":5116},[1933,1934],[1854,5118,1896],{"className":5119},[2018],[1854,5121],{"className":5122,"style":2022},[1939],[1854,5124,5126,5129],{"className":5125},[1933],[1854,5127,2857],{"className":5128,"style":3000},[1933,1934],[1854,5130,5132],{"className":5131},[1968],[1854,5133,5135],{"className":5134},[1972],[1854,5136,5138],{"className":5137},[1977],[1854,5139,5141],{"className":5140,"style":3013},[1981],[1854,5142,5143,5146],{"style":3016},[1854,5144],{"className":5145,"style":1990},[1989],[1854,5147,5149],{"className":5148},[1994,1995,1996,1997],[1854,5150,2860],{"className":5151},[1933,1997],[1854,5153,1911],{"className":5154},[2080],"，则",[1854,5157,5159],{"className":5158},[2118],[1854,5160,5162,5220],{"className":5161},[1857],[1854,5163,5165],{"className":5164},[1861],[1863,5166,5167],{"xmlns":1865,"display":2127},[1867,5168,5169,5217],{},[1870,5170,5171,5197,5199,5215],{},[3081,5172,5173,5191],{},[1870,5174,5175,5177,5179,5181,5183,5185],{},[1877,5176,1883],{"stretchy":1882},[1873,5178,1908],{},[1877,5180,2294],{},[1890,5182,1892],{},[1877,5184,1911],{"stretchy":1882},[2853,5186,5187,5189],{},[1873,5188,3955],{},[1890,5190,2860],{},[2853,5192,5193,5195],{},[1873,5194,2857],{},[1890,5196,2860],{},[1877,5198,2832],{},[5200,5201,5202,5205,5213],"msubsup",{},[1873,5203,5204],{},"χ",[1870,5206,5207,5209,5211],{},[1873,5208,1908],{},[1877,5210,2294],{},[1890,5212,1892],{},[1890,5214,2860],{},[1873,5216,3125],{"mathvariant":2525},[1913,5218,5219],{"encoding":1915},"\\frac{(n-1)S^2}{\\sigma^2}\\sim\\chi^2_{n-1}.",[1854,5221,5223,5379],{"className":5222,"ariaHidden":1895},[1920],[1854,5224,5226,5230,5370,5373,5376],{"className":5225},[1924],[1854,5227],{"className":5228,"style":5229},[1928],"height:2.1771em;vertical-align:-0.686em;",[1854,5231,5233,5236,5367],{"className":5232},[1933],[1854,5234],{"className":5235},[1958,3163],[1854,5237,5239],{"className":5238},[3081],[1854,5240,5242,5358],{"className":5241},[1972,1973],[1854,5243,5245,5355],{"className":5244},[1977],[1854,5246,5249,5289,5297],{"className":5247,"style":5248},[1981],"height:1.4911em;",[1854,5250,5252,5255],{"style":5251},"top:-2.314em;",[1854,5253],{"className":5254,"style":2944},[1989],[1854,5256,5258],{"className":5257},[1933],[1854,5259,5261,5264],{"className":5260},[1933],[1854,5262,2857],{"className":5263,"style":3000},[1933,1934],[1854,5265,5267],{"classN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",[1854,5965,5967,5985],{"className":5966},[1857],[1854,5968,5970],{"className":5969},[1861],[1863,5971,5972],{"xmlns":1865},[1867,5973,5974,5982],{},[1870,5975,5976],{},[2853,5977,5978,5980],{},[1873,5979,2857],{},[1890,5981,2860],{},[1913,5983,5984],{"encoding":1915},"\\sigma^2",[1854,5986,5988],{"className":5987,"ariaHidden":1895},[1920],[1854,5989,5991,5994],{"className":5990},[1924],[1854,5992],{"className":5993,"style":3013},[1928],[1854,5995,5997,6000],{"className":5996},[1933],[1854,5998,2857],{"className":5999,"style":3000},[1933,1934],[1854,6001,6003],{"className":6002},[1968],[1854,6004,6006],{"className":6005},[1972],[1854,6007,6009],{"className":6008},[1977],[1854,6010,6012],{"className":6011,"style":3013},[1981],[1854,6013,6014,6017],{"style":3016},[1854,6015],{"className":6016,"style":1990},[1989],[1854,6018,6020],{"className":6019},[1994,1995,1996,1997],[1854,6021,2860],{"className":6022},[1933,1997]," 的置信区间。由于卡方分布不对称，方差区间一般也不以 ",[1854,6025,6027,6045],{"className":6026},[1857],[1854,6028,6030],{"className":6029},[1861],[1863,6031,6032],{"xmlns":1865},[1867,6033,6034,6042],{},[1870,6035,6036],{},[2853,6037,6038,6040],{},[1873,6039,3955],{},[1890,6041,2860],{},[1913,6043,6044],{"encoding":1915},"S^2",[1854,6046,6048],{"className":6047,"ariaHidden":1895},[1920],[1854,6049,6051,6054],{"className":6050},[1924],[1854,6052],{"className":6053,"style":3013},[1928],[1854,6055,6057,6060],{"className":6056},[1933],[1854,6058,3955],{"className":6059,"style":3970},[1933,1934],[1854,6061,6063],{"className":6062},[1968],[1854,6064,6066],{"className":6065},[1972],[1854,6067,6069],{"className":6068},[1977],[1854,6070,6072],{"className":6071,"style":3013},[1981],[1854,6073,6074,6077],{"style":3016},[1854,6075],{"className":6076,"style":1990},[1989],[1854,6078,6080],{"className":6079},[1994,1995,1996,1997],[1854,6081,2860],{"className":6082},[1933,1997]," 为中心对称。",[1793,6085,6086],{},"若总体不是正态，以上有限样本精确分布通常不成立。样本方差对厚尾和极端值尤其敏感。",[1816,6088,6090],{"id":6089},"_4-两总体参数的区间","4. 两总体参数的区间",[2797,6092,6094],{"id":6093},"_41-独立样本均值差","4.1 独立样本均值差",[1793,6096,6097],{},"两个总体方差不必相等时，Welch 区间为：",[1854,6099,6101],{"className":6100},[2118],[1854,6102,6104,6199],{"className":6103},[1857],[1854,6105,6107],{"className":6106},[1861],[1863,6108,6109],{"xmlns":1865,"display":2127},[1867,6110,6111,6196],{},[1870,6112,6113,6115,6121,6123,6130,6132,6135,6156,6194],{},[1877,6114,1883],{"stretchy":1882},[2826,6116,6117,6119],{"accent":1895},[1873,6118,1875],{},[1877,6120,3091],{},[1877,6122,2294],{},[2826,6124,6125,6128],{"accent":1895},[1873,6126,6127],{},"Y",[1877,6129,3091],{},[1877,6131,1911],{"stretchy":1882},[1877,6133,6134],{},"±",[1885,6136,6137,6139],{},[1873,6138,4051],{},[1870,6140,6141,6143,6145,6147,6149,6151,6153],{},[1890,6142,1892],{},[1877,6144,2294],{},[1873,6146,2297],{},[1873,6148,3102],{"mathvariant":2525},[1890,6150,2860],{},[1877,6152,1896],{"separator":1895},[1873,6154,6155],{},"ν",[3104,6157,6158],{},[1870,6159,6160,6176,6178],{},[3081,6161,6162,6170],{},[5200,6163,6164,6166,6168],{},[1873,6165,3955],{},[1873,6167,1875],{},[1890,6169,2860],{},[1885,6171,6172,6174],{},[1873,6173,1908],{},[1873,6175,1875],{},[1877,6177,3443],{},[3081,6179,6180,6188],{},[5200,6181,6182,6184,6186],{},[1873,6183,3955],{},[1873,6185,6127],{},[1890,6187,2860],{},[1885,6189,6190,6192],{},[1873,6191,1908],{},[1873,6193,6127],{},[1877,6195,1896],{"separator":1895},[1913,6197,6198],{"encoding":1915},"(\\bar X-\\bar Y)\n\\pm t_{1-\\alpha\u002F2,\\nu}\n\\sqrt{\\frac{S_X^2}{n_X}+\\frac{S_Y^2}{n_Y}},",[1854,6200,6202,6252,6302],{"className":6201,"ariaHidden":1895},[1920],[1854,6203,6205,6209,6212,6243,6246,6249],{"className":6204},[1924],[1854,6206],{"className":6207,"style":6208},[1928],"height:1.0701em;vertical-align:-0.25em;",[1854,6210,1883],{"className":6211},[1958],[1854,6213,6215],{"className":6214},[1933,3275],[1854,6216,6218],{"className":6217},[1972],[1854,6219,6221],{"className":6220},[1977],[1854,6222,6224,6232],{"className":6223,"style":3285},[1981],[1854,6225,6226,6229],{"style":2940},[1854,6227],{"className":6228,"style":2944},[1989],[1854,6230,1875],{"className":6231,"style":1935},[1933,1934],[1854,6233,6234,6237],{"style":3296},[1854,6235],{"className":6236,"style":2944},[1989],[1854,6238,6240],{"className":6239,"style":3304},[3303],[1854,6241,3091],{"className":6242},[1933],[1854,6244],{"className":6245,"style":2411},[1939],[1854,6247,2294],{"className":6248},[2415],[1854,6250],{"className":6251,"style":2411},[1939],[1854,6253,6255,6258,6290,6293,6296,6299],{"className":6254},[1924],[1854,6256],{"className":6257,"style":6208},[1928],[1854,6259,6261],{"className":6260},[1933,3275],[1854,6262,6264],{"className":6263},[1972],[1854,6265,6267],{"className":6266},[1977],[1854,6268,6270,6278],{"className":6269,"style":3285},[1981],[1854,6271,6272,6275],{"style":2940},[1854,6273],{"className":6274,"style":2944},[1989],[1854,6276,6127],{"className":6277,"style":2411},[1933,1934],[1854,6279,6280,6283],{"style":3296},[1854,6281],{"className":6282,"style":2944},[1989],[1854,6284,6287],{"className":6285,"style":6286},[3303],"left:-0.25em;",[1854,6288,3091],{"className":6289},[1933],[1854,6291,1911],{"className":6292},[2080],[1854,6294],{"className":6295,"style":2411},[1939],[1854,6297,6134],{"className":6298},[2415],[1854,6300],{"className":6301,"style":2411},[1939],[1854,6303,6305,6309,6368,6731],{"className":6304},[1924],[1854,6306],{"className":6307,"style":6308},[1928],"height:3.04em;vertical-align:-1.0844em;",[1854,6310,6312,6315],{"className":6311},[1933],[1854,6313,4051],{"className":6314},[1933,1934],[1854,6316,6318],{"className":6317},[1968],[1854,6319,6321,6360],{"className":6320},[1972,1973],[1854,6322,6324,6357],{"className":6323},[1977],[1854,6325,6327],{"className":6326,"style":3575},[1981],[1854,6328,6329,6332],{"style":4522},[1854,6330],{"className":6331,"style":1990},[1989],[1854,6333,6335],{"className":6334},[1994,1995,1996,1997],[1854,6336,6338,6341,6344,6347,6350,6353],{"className":6337},[1933,1997],[1854,6339,1892],{"className":6340},[1933,1997],[1854,6342,2294],{"className":6343},[2415,1997],[1854,6345,2297],{"className":6346,"style":2429},[1933,1934,1997],[1854,6348,3600],{"className":6349},[1933,1997],[1854,6351,1896],{"className":6352},[2018,1997],[1854,6354,6155],{"className":6355,"style":6356},[1933,1934,1997],"margin-right:0.0637em;",[1854,6358,2005],{"className":6359},[2004],[1854,6361,6363],{"className":6362},[1977],[1854,6364,6366],{"className":6365,"style":3610},[1981],[1854,6367],{},[1854,6369,6371],{"className":6370},[1933,3195],[1854,6372,6374,6722],{"className":6373},[1972,1973],[1854,6375,6377,6719],{"className":6376},[1977],[1854,6378,6381,6702],{"className":6379,"style":6380},[1981],"height:1.9556em;",[1854,6382,6385,6389],{"className":6383,"style":6384},[3209],"top:-5em;",[1854,6386],{"className":6387,"style":6388},[1989],"height:5em;",[1854,6390,6393,6546,6549,6552,6555],{"className":6391,"style":6392},[1933],"padding-left:1em;",[1854,6394,6396,6399,6543],{"className":6395},[1933],[1854,6397],{"className":6398},[1958,3163],[1854,6400,6402],{"className":6401},[3081],[1854,6403,6405,6534],{"className":6404},[1972,1973],[1854,6406,6408,6531],{"className":6407},[1977],[1854,6409,6412,6461,6469],{"className":6410,"style":6411},[1981],"height:1.4794em;",[1854,6413,6414,6417],{"style":5251},[1854,6415],{"className":6416,"style":2944},[1989],[1854,6418,6420],{"className":6419},[1933],[1854,6421,6423,6426],{"className":6422},[1933],[1854,6424,1908],{"className":6425},[1933,1934],[1854,6427,6429],{"className":6428},[1968],[1854,6430,6432,6453],{"className":6431},[1972,1973],[1854,6433,6435,6450],{"className":6434},[1977],[1854,6436,6439],{"className":6437,"style":6438},[1981],"height:0.3283em;",[1854,6440,6441,6444],{"style":4277},[1854,6442],{"className":6443,"style":1990},[1989],[1854,6445,6447],{"className":6446},[1994,1995,1996,1997],[1854,6448,1875],{"className":6449,"style":1935},[1933,1934,1997],[1854,6451,2005],{"className":6452},[2004],[1854,6454,6456],{"className":6455},[1977],[1854,6457,6459],{"className":6458,"style":2012},[1981],[1854,6460],{},[1854,6462,6463,6466],{"style":3254},[1854,6464],{"className":6465,"style":2944},[1989],[1854,6467],{"className":6468,"style":3262},[3261],[1854,6470,6472,6475],{"style":6471},"top:-3.6835em;",[1854,6473],{"className":6474,"style":2944},[1989],[1854,6476,6478],{"className":6477},[1933],[1854,6479,6481,6484],{"className":6480},[1933],[1854,6482,3955],{"className":6483,"style":3970},[1933,1934],[1854,6485,6487],{"className":6486},[1968],[1854,6488,6490,6522],{"className":6489},[1972,1973],[1854,6491,6493,6519],{"className":6492},[1977],[1854,6494,6496,6508],{"className":6495,"style":5632},[1981],[1854,6497,6499,6502],{"style":6498},"top:-2.4065em;margin-left:-0.0576em;margin-right:0.05em;",[1854,6500],{"className":6501,"style":1990},[1989],[1854,6503,6505],{"className":6504},[1994,1995,1996,1997],[1854,6506,1875],{"className":6507,"style":1935},[1933,1934,1997],[1854,6509,6510,6513],{"style":5671},[1854,6511],{"className":6512,"style":1990},[1989],[1854,6514,6516],{"className":6515},[1994,1995,1996,1997],[1854,6517,2860],{"className":6518},[1933,1997],[1854,6520,2005],{"className":6521},[2004],[1854,6523,6525],{"className":6524},[1977],[1854,6526,6529],{"className":6527,"style":6528},[1981],"height:0.2935em;",[1854,6530],{},[1854,6532,2005],{"className":6533},[2004],[1854,6535,6537],{"className":6536},[1977],[1854,6538,6541],{"className":6539,"style":6540},[1981],"height:0.836em;",[1854,6542],{},[1854,6544],{"className":6545},[2080,3163],[1854,6547],{"className":6548,"style":2411},[1939],[1854,6550,3443],{"className":6551},[2415],[1854,6553],{"className":6554,"style":2411},[1939],[1854,6556,6558,6561,6699],{"className":6557},[1933],[1854,6559],{"className":6560},[1958,3163],[1854,6562,6564],{"className":6563},[3081],[1854,6565,6567,6691],{"className":6566},[1972,1973],[1854,6568,6570,6688],{"className":6569},[1977],[1854,6571,6573,6621,6629],{"className":6572,"style":6411},[1981],[1854,6574,6575,6578],{"style":5251},[1854,6576],{"className":6577,"style":2944},[1989],[1854,6579,6581],{"className":6580},[1933],[1854,6582,6584,6587],{"className":6583},[1933],[1854,6585,1908],{"className":6586},[1933,1934],[1854,6588,6590],{"className":6589},[1968],[1854,6591,6593,6613],{"className":6592},[1972,1973],[1854,6594,6596,6610],{"className":6595},[1977],[1854,6597,6599],{"className":6598,"style":6438},[1981],[1854,6600,6601,6604],{"style":4277},[1854,6602],{"className":6603,"style":1990},[1989],[1854,6605,6607],{"className":6606},[1994,1995,1996,1997],[1854,6608,6127],{"className":6609,"style":2411},[1933,1934,1997],[1854,6611,2005],{"className":6612},[2004],[1854,6614,6616],{"className":6615},[1977],[1854,6617,6619],{"className":6618,"style":2012},[1981],[1854,6620],{},[1854,6622,6623,6626],{"style":3254},[1854,6624],{"className":6625,"style":2944},[1989],[1854,6627],{"className":6628,"style":3262},[3261],[1854,6630,6631,6634],{"style":6471},[1854,6632],{"className":6633,"style":2944},[1989],[1854,6635,6637],{"className":6636},[1933],[1854,6638,6640,6643],{"className":6639},[1933],[1854,6641,3955],{"className":6642,"style":3970},[1933,1934],[1854,6644,6646],{"className":6645},[1968],[1854,6647,6649,6680],{"className":6648},[1972,1973],[1854,6650,6652,6677],{"className":6651},[1977],[1854,6653,6655,6666],{"className":6654,"style":5632},[1981],[1854,6656,6657,6660],{"style":6498},[1854,6658],{"className":6659,"style":1990},[1989],[1854,6661,6663],{"className":6662},[1994,1995,1996,1997],[1854,6664,6127],{"className":6665,"style":2411},[1933,1934,1997],[1854,6667,6668,6671],{"style":5671},[1854,6669],{"className":6670,"style":1990},[1989],[1854,6672,6674],{"className":6673},[1994,1995,1996,1997],[1854,6675,2860],{"className":6676},[1933,1997],[1854,6678,2005],{"className":6679},[2004],[1854,6681,6683],{"className":6682},[1977],[1854,6684,6686],{"className":6685,"style":6528},[1981],[1854,6687],{},[1854,6689,2005],{"className":6690},[2004],[1854,6692,6694],{"className":6693},[1977],[1854,6695,6697],{"className":6696,"style":6540},[1981],[1854,6698],{},[1854,6700],{"className":6701},[2080,3163],[1854,6703,6705,6708],{"style":6704},"top:-3.9156em;",[1854,6706],{"className":6707,"style":6388},[1989],[1854,6709,6712],{"className":6710,"style":6711},[3226],"min-width:1.02em;height:3.08em;",[3229,6713,6716],{"xmlns":3231,"width":3232,"height":6714,"viewBox":6715,"preserveAspectRatio":3235},"3.08em","0 0 400000 3240",[3237,6717],{"d":6718},"M473,2793\nc339.3,-1799.3,509.3,-2700,510,-2702 l0 -0\nc3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7\ns-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200\nc0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26\ns76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,\n606zM1001 80h400000v40H1017.7z",[1854,6720,2005],{"className":6721},[2004],[1854,6723,6725],{"className":6724},[1977],[1854,6726,6729],{"className":6727,"style":6728},[1981],"height:1.0844em;",[1854,6730],{},[1854,6732,1896],{"className":6733},[2018],[1793,6735,6736,6737,6766],{},"其中自由度 ",[1854,6738,6740,6754],{"className":6739},[1857],[1854,6741,6743],{"className":6742},[1861],[1863,6744,6745],{"xmlns":1865},[1867,6746,6747,6751],{},[1870,6748,6749],{},[1873,6750,6155],{},[1913,6752,6753],{"encoding":1915},"\\nu",[1854,6755,6757],{"className":6756,"ariaHidden":1895},[1920],[1854,6758,6760,6763],{"className":6759},[1924],[1854,6761],{"className":6762,"style":2484},[1928],[1854,6764,6155],{"className":6765,"style":6356},[1933,1934]," 用 Welch–Satterthwaite 近似。除非有充分证据支持方差相等，实践中通常优先使用 Welch 方法。",[2797,6768,6770],{"id":6769},"_42-配对样本","4.2 配对样本",[1793,6772,6773,6774,6974,6975,7020],{},"对同一对象前后测量时，应先构造差值 ",[1854,6775,6777,6812],{"className":6776},[1857],[1854,6778,6780],{"className":6779},[1861],[1863,6781,6782],{"xmlns":1865},[1867,6783,6784,6809],{},[1870,6785,6786,6793,6795,6801,6803],{},[1885,6787,6788,6791],{},[1873,6789,6790],{},"D",[1873,6792,2822],{},[1877,6794,1879],{},[1885,6796,6797,6799],{},[1873,6798,1875],{},[1873,6800,2822],{},[1877,6802,2294],{},[1885,6804,6805,6807],{},[1873,6806,6127],{},[1873,6808,2822],{},[1913,6810,6811],{"encoding":1915},"D_i=X_i-Y_i",[1854,6813,6815,6872,6927],{"className":6814,"ariaHidden":1895},[1920],[1854,6816,6818,6822,6863,6866,6869],{"className":6817},[1924],[1854,6819],{"className":6820,"style":6821},[1928],"height:0.8333em;vertical-align:-0.15em;",[1854,6823,6825,6828],{"className":6824},[1933],[1854,6826,6790],{"className":6827,"style":2113},[1933,1934],[1854,6829,6831],{"className":6830},[1968],[1854,6832,6834,6855],{"className":6833},[1972,1973],[1854,6835,6837,6852],{"className":6836},[1977],[1854,6838,6840],{"className":6839,"style":2894},[1981],[1854,6841,6843,6846],{"style":6842},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1854,6844],{"className":6845,"style":1990},[1989],[1854,6847,6849],{"className":6848},[1994,1995,1996,1997],[1854,6850,2822],{"className":6851},[1933,1934,1997],[1854,6853,2005],{"className":6854},[2004],[1854,6856,6858],{"className":6857},[1977],[1854,6859,6861],{"className":6860,"style":2012},[1981],[1854,6862],{},[1854,6864],{"className":6865,"style":1940},[1939],[1854,6867,1879],{"className":6868},[1944],[1854,6870],{"className":6871,"style":1940},[1939],[1854,6873,6875,6878,6918,6921,6924],{"className":6874},[1924],[1854,6876],{"className":6877,"style":6821},[1928],[1854,6879,6881,6884],{"className":6880},[1933],[1854,6882,1875],{"className":6883,"style":1935},[1933,1934],[1854,6885,6887],{"className":6886},[1968],[1854,6888,6890,6910],{"className":6889},[1972,1973],[1854,6891,6893,6907],{"className":6892},[1977],[1854,6894,6896],{"className":6895,"style":2894},[1981],[1854,6897,6898,6901],{"style":1985},[1854,6899],{"className":6900,"style":1990},[1989],[1854,6902,6904],{"className":6903},[1994,1995,1996,1997],[1854,6905,2822],{"className":6906},[1933,1934,1997],[1854,6908,2005],{"className":6909},[2004],[1854,6911,6913],{"className":6912},[1977],[1854,6914,6916],{"className":6915,"style":2012},[1981],[1854,6917],{},[1854,6919],{"className":6920,"style":2411},[1939],[1854,6922,2294],{"className":6923},[2415],[1854,6925],{"className":6926,"style":2411},[1939],[1854,6928,6930,6933],{"className":6929},[1924],[1854,6931],{"className":6932,"style":6821},[1928],[1854,6934,6936,6939],{"className":6935},[1933],[1854,6937,6127],{"className":6938,"style":2411},[1933,1934],[1854,6940,6942],{"className":6941},[1968],[1854,6943,6945,6966],{"className":6944},[1972,1973],[1854,6946,6948,6963],{"className":6947},[1977],[1854,6949,6951],{"className":6950,"style":2894},[1981],[1854,6952,6954,6957],{"style":6953},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[1854,6955],{"className":6956,"style":1990},[1989],[1854,6958,6960],{"className":6959},[1994,1995,1996,1997],[1854,6961,2822],{"className":6962},[1933,1934,1997],[1854,6964,2005],{"className":6965},[2004],[1854,6967,6969],{"className":6968},[1977],[1854,6970,6972],{"className":6971,"style":2012},[1981],[1854,6973],{},"，再对 ",[1854,6976,6978,6999],{"className":6977},[1857],[1854,6979,6981],{"className":6980},[1861],[1863,6982,6983],{"xmlns":1865},[1867,6984,6985,6996],{},[1870,6986,6987,6990,6992,6994],{},[1873,6988,6989],{},"E",[1877,6991,2145],{"stretchy":1882},[1873,6993,6790],{},[1877,6995,2168],{"stretchy":1882},[1913,6997,6998],{"encoding":1915},"E[D]",[1854,7000,7002],{"className":7001,"ariaHidden":1895},[1920],[1854,7003,7005,7008,7011,7014,7017],{"className":7004},[1924],[1854,7006],{"className":7007,"style":1954},[1928],[1854,7009,6989],{"className":7010,"style":3970},[1933,1934],[1854,7012,2145],{"className":7013},[1958],[1854,7015,6790],{"className":7016,"style":2113},[1933,1934],[1854,7018,2168],{"className":7019},[2080]," 构造单样本 t 区间。配对设计利用个体内相关性，不能把两列数据当独立样本。",[2797,7022,7024],{"id":7023},"_43-两个比例之差","4.3 两个比例之差",[1793,7026,7027],{},"大样本 Wald 区间为：",[1854,7029,7031],{"className":7030},[2118],[1854,7032,7034,7175],{"className":7033},[1857],[1854,7035,7037],{"className":7036},[1861],[1863,7038,7039],{"xmlns":1865,"display":2127},[1867,7040,7041,7172],{},[1870,7042,7043,7045,7056,7058,7068,7070,7072,7088,7170],{},[1877,7044,1883],{"stretchy":1882},[1885,7046,7047,7054],{},[2826,7048,7049,7051],{"accent":1895},[1873,7050,1793],{},[1877,7052,7053],{},"^",[1890,7055,1892],{},[1877,7057,2294],{},[1885,7059,7060,7066],{},[2826,7061,7062,7064],{"accent":1895},[1873,7063,1793],{},[1877,7065,7053],{},[1890,7067,2860],{},[1877,7069,1911],{"stretchy":1882},[1877,7071,6134],{},[1885,7073,7074,7076],{},[1873,7075,3412],{},[1870,7077,7078,7080,7082,7084,7086],{},[1890,7079,1892],{},[1877,7081,2294],{},[1873,7083,2297],{},[1873,7085,3102],{"mathvariant":2525},[1890,7087,2860],{},[3104,7089,7090],{},[1870,7091,7092,7130,7132],{},[3081,7093,7094,7124],{},[1870,7095,7096,7106,7108,7110,7112,7122],{},[1885,7097,7098,7104],{},[2826,7099,7100,7102],{"accent":1895},[1873,7101,1793],{},[1877,7103,7053],{},[1890,7105,1892],{},[1877,7107,1883],{"stretchy":1882},[1890,7109,1892],{},[1877,7111,2294],{},[1885,7113,7114,7120],{},[2826,7115,7116,7118],{"accent":1895},[1873,7117,1793],{},[1877,7119,7053],{},[1890,7121,1892],{},[1877,7123,1911],{"stretchy":1882},[1885,7125,7126,7128],{},[1873,7127,1908],{},[1890,7129,1892],{},[1877,7131,3443],{},[3081,7133,7134,7164],{},[1870,7135,7136,7146,7148,7150,7152,7162],{},[1885,7137,7138,7144],{},[2826,7139,7140,7142],{"accent":1895},[1873,7141,1793],{},[1877,7143,7053],{},[1890,7145,2860],{},[1877,7147,1883],{"stretchy":1882},[1890,7149,1892],{},[1877,7151,2294],{},[1885,7153,7154,7160],{},[2826,7155,7156,7158],{"accent":1895},[1873,7157,1793],{},[1877,7159,7053],{},[1890,7161,2860],{},[1877,7163,1911],{"stretchy":1882},[1885,7165,7166,7168],{},[1873,7167,1908],{},[1890,7169,2860],{},[1873,7171,3125],{"mathvariant":2525},[1913,7173,7174],{"encoding":1915},"(\\hat p_1-\\hat p_2)\n\\pm z_{1-\\alpha\u002F2}\n\\sqrt{\\frac{\\hat p_1(1-\\hat p_1)}{n_1}\n+\\frac{\\hat p_2(1-\\hat p_2)}{n_2}}.",[1854,7176,7178,7276,7373],{"className":7177,"ariaHidden":1895},[1920],[1854,7179,7181,7184,7187,7267,7270,7273],{"className":7180},[1924],[1854,7182],{"className":7183,"style":1954},[1928],[1854,7185,1883],{"className":7186},[1958],[1854,7188,7190,7233],{"className":7189},[1933],[1854,7191,7193],{"className":7192},[1933,3275],[1854,7194,7196,7224],{"className":7195},[1972,1973],[1854,7197,7199,7221],{"className":7198},[1977],[1854,7200,7202,7210],{"className":7201,"style":2109},[1981],[1854,7203,7204,7207],{"style":2940},[1854,7205],{"className":7206,"style":2944},[1989],[1854,7208,1793],{"className":7209},[1933,1934],[1854,7211,7212,7215],{"style":2940},[1854,7213],{"className":7214,"style":2944},[1989],[1854,7216,7218],{"className":7217,"style":3304},[3303],[1854,7219,7053],{"className":7220},[1933],[1854,7222,2005],{"className":7223},[2004],[1854,7225,7227],{"className":7226},[1977],[1854,7228,7231],{"className":7229,"style":7230},[1981],"height:0.1944em;",[1854,7232],{},[1854,7234,7236],{"className":7235},[1968],[1854,7237,7239,7259],{"className":7238},[1972,1973],[1854,7240,7242,7256],{"className":7241},[1977],[1854,7243,7245],{"className":7244,"style":1982},[1981],[1854,7246,7247,7250],{"style":4277},[1854,7248],{"className":7249,"style":1990},[1989],[1854,7251,7253],{"className":7252},[1994,1995,1996,1997],[1854,7254,1892],{"className":7255},[1933,1997],[1854,7257,2005],{"className":7258},[2004],[1854,7260,7262],{"className":7261},[1977],[1854,7263,7265],{"className":7264,"style":2012},[1981],[1854,7266],{},[1854,7268],{"className":7269,"style":2411},[1939],[1854,7271,2294],{"className":7272},[2415],[1854,7274],{"className":7275,"style":2411},[1939],[1854,7277,7279,7282,7361,7364,7367,7370],{"className":7278},[1924],[1854,7280],{"className":7281,"style":1954},[1928],[1854,7283,7285,7327],{"className":7284},[1933],[1854,7286,7288],{"className":7287},[1933,3275],[1854,7289,7291,7319],{"className":7290},[1972,1973],[1854,7292,7294,7316],{"className":7293},[1977],[1854,7295,7297,7305],{"className":7296,"style":2109},[1981],[1854,7298,7299,7302],{"style":2940},[1854,7300],{"className":7301,"style":2944},[1989],[1854,7303,1793],{"className":7304},[1933,1934],[1854,7306,7307,7310],{"style":2940},[1854,7308],{"className":7309,"style":2944},[1989],[1854,7311,7313],{"className":7312,"style":3304},[3303],[1854,7314,7053],{"className":7315},[1933],[1854,7317,2005],{"className":7318},[2004],[1854,7320,7322],{"className":7321},[1977],[1854,7323,7325],{"className":7324,"style":7230},[1981],[1854,7326],{},[1854,7328,7330],{"className":7329},[1968],[1854,7331,7333,7353],{"className":7332},[1972,1973],[1854,7334,7336,7350],{"className":7335},[1977],[1854,7337,7339],{"className":7338,"style":1982},[1981],[1854,7340,7341,7344],{"style":4277},[1854,7342],{"className":7343,"style":1990},[1989],[1854,7345,7347],{"className":7346},[1994,1995,1996,1997],[1854,7348,2860],{"className":7349},[1933,1997],[1854,7351,2005],{"className":7352},[2004],[1854,7354,7356],{"className":7355},[1977],[1854,7357,7359],{"className":7358,"style":2012},[1981],[1854,7360],{},[1854,7362,1911],{"className":7363},[2080],[1854,7365],{"className":7366,"style":2411},[1939],[1854,7368,6134],{"className":7369},[2415],[1854,7371],{"className":7372,"style":2411},[1939],[1854,7374,7376,7380,7432,8033],{"className":7375},[1924],[1854,7377],{"className":7378,"style":7379},[1928],"height:3.04em;vertical-align:-1.1106em;",[1854,7381,7383,7386],{"className":7382},[1933],[1854,7384,3412],{"className":7385,"style":3562},[1933,1934],[1854,7387,7389],{"className":7388},[1968],[1854,7390,7392,7424],{"className":7391},[1972,1973],[1854,7393,7395,7421],{"className":7394},[1977],[1854,7396,7398],{"className":7397,"style":3575},[1981],[1854,7399,7400,7403],{"style":3578},[1854,7401],{"className":7402,"style":1990},[1989],[1854,7404,7406],{"className":7405},[1994,1995,1996,1997],[1854,7407,7409,7412,7415,7418],{"className":7408},[1933,1997],[1854,7410,1892],{"className":7411},[1933,1997],[1854,7413,2294],{"className":7414},[2415,1997],[1854,7416,2297],{"className":7417,"style":2429},[1933,1934,1997],[1854,7419,3600],{"className":7420},[1933,1997],[1854,7422,2005],{"className":7423},[2004],[1854,7425,7427],{"className":7426},[1977],[1854,7428,7430],{"className":7429,"style":3610},[1981],[1854,7431],{},[1854,7433,7435],{"className":7434},[1933,3195],[1854,7436,7438,8024],{"className":7437},[1972,1973],[1854,7439,7441,8021],{"className":7440},[1977],[1854,7442,7445,8008],{"className":7443,"style":7444},[1981],"height:1.9294em;",[1854,7446,7448,7451],{"className":7447,"style":6384},[3209],[1854,7449],{"className":7450,"style":6388},[1989],[1854,7452,7454,7727,7730,7733,7736],{"className":7453,"style":6392},[1933],[1854,7455,7457,7460,7724],{"className":7456},[1933],[1854,7458],{"className":7459},[1958,3163],[1854,7461,7463],{"className":7462},[3081],[1854,7464,7466,7716],{"className":7465},[1972,1973],[1854,7467,7469,7713],{"className":7468},[1977],[1854,7470,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区间为：",[1854,8047,8049],{"className":8048},[2118],[1854,8050,8052,8118],{"className":8051},[1857],[1854,8053,8055],{"className":8054},[1861],[1863,8056,8057],{"xmlns":1865,"display":2127},[1867,8058,8059,8115],{},[1870,8060,8061,8067,8069,8085,8113],{},[2826,8062,8063,8065],{"accent":1895},[1873,8064,1793],{},[1877,8066,7053],{},[1877,8068,6134],{},[1885,8070,8071,8073],{},[1873,8072,3412],{},[1870,8074,8075,8077,8079,8081,8083],{},[1890,8076,1892],{},[1877,8078,2294],{},[1873,8080,2297],{},[1873,8082,3102],{"mathvariant":2525},[1890,8084,2860],{},[3104,8086,8087],{},[3081,8088,8089,8111],{},[1870,8090,8091,8097,8099,8101,8103,8109],{},[2826,8092,8093,8095],{"accent":1895},[1873,8094,1793],{},[1877,8096,7053],{},[1877,8098,1883],{"stretchy":1882},[1890,8100,1892],{},[1877,8102,2294],{},[2826,8104,8105,8107],{"accent":1895},[1873,8106,1793],{},[1877,8108,7053],{},[1877,8110,1911],{"stretchy":1882},[1873,8112,1908],{},[1873,8114,3125],{"mathvariant":2525},[1913,8116,8117],{"encoding":1915},"\\hat p\\pm z_{1-\\alpha\u002F2}\n\\sqrt{\\frac{\\hat p(1-\\hat p)}{n}}.",[1854,8119,8121,8179],{"className":8120,"ariaHidden":1895},[1920],[1854,8122,8124,8128,8170,8173,8176],{"className":8123},[1924],[1854,8125],{"className":8126,"style":8127},[1928],"height:0.8889em;vertical-align:-0.1944em;",[1854,8129,8131],{"className":8130},[1933,3275],[1854,8132,8134,8162],{"className":8133},[1972,1973],[1854,8135,8137,8159],{"className":8136},[1977],[1854,8138,8140,8148],{"className":8139,"style":2109},[1981],[1854,8141,8142,8145],{"style":2940},[1854,8143],{"className":8144,"style":2944},[1989],[1854,8146,1793],{"className":8147},[1933,1934],[1854,8149,8150,8153],{"style":2940},[1854,8151],{"className":8152,"style":2944},[1989],[1854,8154,8156],{"className":8155,"style":3304},[3303],[1854,8157,7053],{"className":8158},[1933],[1854,8160,2005],{"className":8161},[2004],[1854,8163,8165],{"className":8164},[1977],[1854,8166,8168],{"className":8167,"style":7230},[1981],[1854,8169],{},[1854,8171],{"className":8172,"style":2411},[1939],[1854,8174,6134],{"className":8175},[2415],[1854,8177],{"className":8178,"style":2411},[1939],[1854,8180,8182,8186,8238,8452],{"className":8181},[1924],[1854,8183],{"className":8184,"style":8185},[1928],"height:2.44em;vertical-align:-0.7356em;",[1854,8187,8189,8192],{"className":8188},[1933],[1854,8190,3412],{"className":8191,"style":3562},[1933,1934],[1854,8193,8195],{"className":8194},[1968],[1854,8196,8198,8230],{"className":8197},[1972,1973],[1854,8199,8201,8227],{"className":8200},[1977],[1854,8202,8204],{"className":8203,"style":3575},[1981],[1854,8205,8206,8209],{"style":3578},[1854,8207],{"className":8208,"style":1990},[1989],[1854,8210,8212],{"className":8211},[1994,1995,1996,1997],[1854,8213,8215,8218,8221,8224],{"className":8214},[1933,1997],[1854,8216,1892],{"className":8217},[1933,1997],[1854,8219,2294],{"className":8220},[2415,1997],[1854,8222,2297],{"className":8223,"style":2429},[1933,1934,1997],[1854,8225,3600],{"className":8226},[1933,1997],[1854,8228,2005],{"className":8229},[2004],[1854,8231,8233],{"className":8232},[1977],[1854,8234,8236],{"className":8235,"style":3610},[1981],[1854,8237],{},[1854,8239,8241],{"className":8240},[1933,3195],[1854,8242,8244,8443],{"className":8243},[1972,1973],[1854,8245,8247,8440],{"className":8246},[1977],[1854,8248,8251,8423],{"className":8249,"style":8250},[1981],"height:1.7044em;",[1854,8252,8255,8259],{"className":8253,"style":8254},[3209],"top:-4.4em;",[1854,8256],{"className":8257,"style":8258},[1989],"height:4.4em;",[1854,8260,8262],{"className":8261,"style":6392},[1933],[1854,8263,8265,8268,8420],{"className":8264},[1933],[1854,8266],{"className":8267},[1958,3163],[1854,8269,8271],{"className":8270},[3081],[1854,8272,8274,8412],{"className":8273},[1972,1973],[1854,8275,8277,8409],{"className":8276},[1977],[1854,8278,8280,8291,8299],{"className":8279,"style":7472},[1981],[1854,8281,8282,8285],{"style":5251},[1854,8283],{"className":8284,"style":2944},[1989],[1854,8286,8288],{"className":8287},[1933],[1854,8289,1908],{"className":8290},[1933,1934],[1854,8292,8293,8296],{"style":3254},[1854,8294],{"className":8295,"style":2944},[1989],[1854,8297],{"className":8298,"style":3262},[3261],[1854,8300,8301,8304],{"style":3265},[1854,8302],{"className":8303,"style":2944},[1989],[1854,8305,8307,8349,8352,8355,8358,8361,8364,8406],{"className":8306},[1933],[1854,8308,8310],{"className":8309},[1933,3275],[1854,8311,8313,8341],{"className":8312},[1972,1973],[1854,8314,8316,8338],{"className":8315},[1977],[1854,8317,8319,8327],{"className":8318,"style":2109},[1981],[1854,8320,8321,8324],{"style":2940},[1854,8322],{"className":8323,"style":2944},[1989],[1854,8325,1793],{"className":8326},[1933,1934],[1854,8328,8329,8332],{"style":2940},[1854,8330],{"className":8331,"style":2944},[1989],[1854,8333,8335],{"className":8334,"style":3304},[3303],[1854,8336,7053],{"className":8337},[1933],[1854,8339,2005],{"className":8340},[2004],[1854,8342,8344],{"className":8343},[1977],[1854,8345,8347],{"className":8346,"style":7230},[1981],[1854,8348],{},[1854,8350,1883],{"className":8351},[1958],[1854,8353,1892],{"className":8354},[1933],[1854,8356],{"className":8357,"style":2411},[1939],[1854,8359,2294],{"className":8360},[2415],[1854,8362],{"className":8363,"style":2411},[1939],[1854,8365,8367],{"className":8366},[1933,3275],[1854,8368,8370,8398],{"className":8369},[1972,1973],[1854,8371,8373,8395],{"className":8372},[1977],[1854,8374,8376,8384],{"className":8375,"style":2109},[1981],[1854,8377,8378,8381],{"style":2940},[1854,8379],{"className":8380,"style":2944},[1989],[1854,8382,1793],{"className":8383},[1933,1934],[1854,8385,8386,8389],{"style":2940},[1854,8387],{"className":8388,"style":2944},[1989],[1854,8390,8392],{"className":8391,"style":3304},[3303],[1854,8393,7053],{"className":8394},[1933],[1854,8396,2005],{"className":8397},[2004],[1854,8399,8401],{"className":8400},[1977],[1854,8402,8404],{"className":8403,"style":7230},[1981],[1854,8405],{},[1854,8407,1911],{"className":8408},[2080],[1854,8410,2005],{"class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873,9012,3412],{},[1890,9014,2860],{},[1870,9016,9017,9020],{},[1890,9018,9019],{},"4",[2853,9021,9022,9024],{},[1873,9023,1908],{},[1890,9025,2860],{},[1873,9027,3125],{"mathvariant":2525},[1913,9029,9030],{"encoding":1915},"\\text{half-width}\n=\\frac{z}{1+z^2\u002Fn}\n\\sqrt{\\frac{\\hat p(1-\\hat p)}{n}+\\frac{z^2}{4n^2}}.",[1854,9032,9034,9055],{"className":9033,"ariaHidden":1895},[1920],[1854,9035,9037,9040,9046,9049,9052],{"className":9036},[1924],[1854,9038],{"className":9039,"style":2109},[1928],[1854,9041,9043],{"className":9042},[1933,8713],[1854,9044,8952],{"className":9045},[1933],[1854,9047],{"className":9048,"style":1940},[1939],[1854,9050,1879],{"className":9051},[1944],[1854,9053],{"className":9054,"style":1940},[1939],[1854,9056,9058,9062,9168,9500],{"className":9057},[1924],[1854,9059],{"className":9060,"style":9061},[1928],"height:2.6404em;vertical-align:-0.936em;",[1854,9063,9065,9068,9165],{"className":9064},[1933],[1854,9066],{"className":9067},[1958,3163],[1854,9069,9071],{"className":9070},[3081],[1854,9072,9074,9157],{"className":9073},[1972,1973],[1854,9075,9077,9154],{"className":9076},[1977],[1854,9078,9080,9135,9143],{"className":9079,"style":3631},[1981],[1854,9081,9082,9085],{"style":5251},[1854,9083],{"className":9084,"style":2944},[1989],[1854,9086,9088,9091,9094,9097,9100,9129,9132],{"className":9087},[1933],[1854,9089,1892],{"className":9090},[1933],[1854,9092],{"className":9093,"style":2411},[1939],[1854,9095,3443],{"className":9096},[2415],[1854,9098],{"className":9099,"style":2411},[1939],[1854,9101,9103,9106],{"className":9102},[1933],[1854,9104,3412],{"className":9105,"style":3562},[1933,1934],[1854,9107,9109],{"className":9108},[1968],[1854,9110,9112],{"className":9111},[1972],[1854,9113,9115],{"className":9114},[1977],[1854,9116,9118],{"className":9117,"style":5276},[1981],[1854,9119,9120,9123],{"style":5279},[1854,9121],{"className":9122,"style":1990},[1989],[1854,9124,9126],{"className":9125},[1994,1995,1996,1997],[1854,9127,2860],{"className":9128},[1933,1997],[1854,9130,3102],{"className":9131},[1933],[1854,9133,1908],{"className":9134},[1933,1934],[1854,9136,9137,9140],{"style":3254},[1854,9138],{"className":9139,"style":2944},[1989],[1854,9141],{"className":9142,"style":3262},[3261],[1854,9144,9145,9148],{"style":3265},[1854,9146],{"className":9147,"style":2944},[1989],[1854,9149,9151],{"className":9150},[1933],[1854,9152,3412],{"className":9153,"style":3562},[1933,1934],[1854,9155,2005],{"className":9156},[2004],[1854,9158,9160],{"className":9159},[1977],[1854,9161,9163],{"className":9162,"style":8926},[1981],[1854,9164],{},[1854,9166],{"className":9167},[2080,3163],[1854,9169,9171],{"className":9170},[1933,3195],[1854,9172,9174,9492],{"className":9173},[1972,1973],[1854,9175,9177,9489],{"className":9176},[1977],[1854,9178,9180,9477],{"className":9179,"style":8250},[1981],[1854,9181,9183,9186],{"className":9182,"style":8254},[3209],[1854,9184],{"className":9185,"style":8258},[1989],[1854,9187,9189,9350,9353,9356,9359],{"className":9188,"style":6392},[1933],[1854,9190,9192,9195,9347],{"className":9191},[1933],[1854,9193],{"className":9194},[1958,3163],[1854,9196,9198],{"className":9197},[3081],[1854,9199,9201,9339],{"className":9200},[1972,1973],[1854,9202,9204,9336],{"className":9203},[1977],[1854,9205,9207,9218,9226],{"className":9206,"style":7472},[1981],[1854,9208,9209,9212],{"style":5251},[1854,9210],{"className":9211,"style":2944},[1989],[1854,9213,9215],{"className":9214},[1933],[1854,9216,1908],{"className":9217},[1933,1934],[1854,9219,9220,9223],{"style":3254},[1854,9221],{"className":9222,"style":2944},[1989],[1854,9224],{"className":9225,"style":3262},[3261],[1854,9227,9228,9231],{"style":3265},[1854,9229],{"className":9230,"style":2944},[1989],[1854,9232,9234,9276,9279,9282,9285,9288,9291,9333],{"className":9233},[1933],[1854,9235,9237],{"className":9236},[1933,3275],[1854,9238,9240,9268],{"className":9239},[1972,1973],[1854,9241,9243,9265],{"className":9242},[1977],[1854,9244,9246,9254],{"className":9245,"style":2109},[1981],[1854,9247,9248,9251],{"style":2940},[1854,9249],{"className":9250,"style":2944},[1989],[1854,9252,1793],{"className":9253},[1933,1934],[1854,9255,9256,9259],{"style":2940},[1854,9257],{"className":9258,"style":2944},[1989],[1854,9260,9262],{"className":9261,"style":3304},[3303],[1854,9263,7053],{"className":9264},[1933],[1854,9266,2005],{"className":9267},[2004],[1854,9269,9271],{"className":9270},[1977],[1854,9272,9274],{"className":9273,"style":7230},[1981],[1854,9275],{},[1854,9277,1883],{"className":9278},[1958],[1854,9280,1892],{"className":9281},[1933],[1854,9283],{"className":9284,"style":2411},[1939],[1854,9286,2294],{"className":9287},[2415],[1854,9289],{"className":9290,"style":2411},[1939],[1854,9292,9294],{"className":9293},[1933,3275],[1854,9295,9297,9325],{"className":9296},[1972,1973],[1854,9298,9300,9322],{"className":9299},[1977],[1854,9301,9303,9311],{"className":9302,"style":2109},[1981],[1854,9304,9305,9308],{"style":2940},[1854,9306],{"className":9307,"style":2944},[1989],[1854,9309,1793],{"className":9310},[1933,1934],[1854,9312,9313,9316],{"style":2940},[1854,9314],{"className":9315,"style":2944},[1989],[1854,9317,9319],{"className":9318,"style":3304},[3303],[1854,9320,7053],{"className":9321},[1933],[1854,9323,2005],{"className":9324},[2004],[1854,9326,9328],{"className":9327},[1977],[1854,9329,9331],{"className":9330,"style":7230},[1981],[1854,9332],{},[1854,9334,1911],{"className":9335},[2080],[1854,9337,2005],{"className":9338},[2004],[1854,9340,9342],{"className":9341},[1977],[1854,9343,9345],{"className":9344,"style":5364},[1981],[1854,9346],{},[1854,9348],{"className":9349},[2080,3163],[1854,9351],{"className":9352,"style":2411},[1939],[1854,9354,3443],{"className":9355},[2415],[1854,9357],{"className":9358,"style":2411},[1939],[1854,9360,9362,9365,9474],{"className":9361},[1933],[1854,9363],{"className":9364},[1958,3163],[1854,9366,9368],{"className":9367},[3081],[1854,9369,9371,9466],{"className":9370},[1972,1973],[1854,9372,9374,9463],{"className":9373},[1977],[1854,9375,9378,9418,9426],{"className":9376,"style":9377},[1981],"height:1.4171em;",[1854,9379,9380,9383],{"style":5251},[1854,9381],{"className":9382,"style":2944},[1989],[1854,9384,9386,9389],{"className":9385},[1933],[1854,9387,9019],{"className":9388},[1933],[1854,9390,9392,9395],{"className":9391},[1933],[1854,9393,1908],{"className":9394},[1933,1934],[1854,9396,9398],{"className":9397},[1968],[1854,9399,9401],{"className":9400},[1972],[1854,9402,9404],{"className":9403},[1977],[1854,9405,9407],{"className":9406,"style":5276},[1981],[1854,9408,9409,9412],{"style":5279},[1854,9410],{"className":9411,"style":1990},[1989],[1854,9413,9415],{"className":9414},[1994,1995,1996,1997],[1854,9416,2860],{"className":9417},[1933,1997],[1854,9419,9420,9423],{"style":3254},[1854,9421],{"className":9422,"style":2944},[1989],[1854,9424],{"className":9425,"style":3262},[3261],[1854,9427,9428,9431],{"style":3265},[1854,9429],{"className":9430,"style":2944},[1989],[1854,9432,9434],{"className":9433},[1933],[1854,9435,9437,9440],{"className":9436},[1933],[1854,9438,3412],{"className":9439,"style":3562},[1933,1934],[1854,9441,9443],{"className":9442},[1968],[1854,9444,9446],{"className":9445},[1972],[1854,9447,9449],{"className":9448},[1977],[1854,9450,9452],{"className":9451,"style":5276},[1981],[1854,9453,9454,9457],{"style":5279},[1854,9455],{"className":9456,"style":1990},[1989],[1854,9458,9460],{"className":9459},[1994,1995,1996,1997],[1854,9461,2860],{"className":9462},[1933,1997],[1854,9464,2005],{"className":9465},[2004],[1854,9467,9469],{"className":9468},[1977],[1854,9470,9472],{"className":9471,"style":5364},[1981],[1854,9473],{},[1854,9475],{"className":9476},[2080,3163],[1854,9478,9479,9482],{"style":8425},[1854,9480],{"className":9481,"style":8258},[1989],[1854,9483,9485],{"className":9484,"style":8432},[3226],[3229,9486,9487],{"xmlns":3231,"width":3232,"height":8435,"viewBox":8436,"preserveAspectRatio":3235},[3237,9488],{"d":8439},[1854,9490,2005],{"className":9491},[2004],[1854,9493,9495],{"className":9494},[1977],[1854,9496,9498],{"className":9497,"style":8449},[1981],[1854,9499],{},[1854,9501,3125],{"className":9502},[1933],[1793,9504,9505],{},"Wilson 区间自动保持在合理范围附近，有限样本覆盖通常更好。",[2797,9507,9508],{"id":9508},"覆盖率实验",[1793,9510,9511,9512,9565,9566,9618],{},"下面设 ",[1854,9513,9515,9534],{"className":9514},[1857],[1854,9516,9518],{"className":9517},[1861],[1863,9519,9520],{"xmlns":1865},[1867,9521,9522,9531],{},[1870,9523,9524,9526,9528],{},[1873,9525,1908],{},[1877,9527,1879],{},[1890,9529,9530],{},"30",[1913,9532,9533],{"encoding":1915},"n=30",[1854,9535,9537,9555],{"className":9536,"ariaHidden":1895},[1920],[1854,9538,9540,9543,9546,9549,9552],{"className":9539},[1924],[1854,9541],{"className":9542,"style":2484},[1928],[1854,9544,1908],{"className":9545},[1933,1934],[1854,9547],{"className":9548,"style":1940},[1939],[1854,9550,1879],{"className":9551},[1944],[1854,9553],{"className":9554,"style":1940},[1939],[1854,9556,9558,9562],{"className":9557},[1924],[1854,9559],{"className":9560,"style":9561},[1928],"height:0.6444em;",[1854,9563,9530],{"className":9564},[1933],"、真比例 ",[1854,9567,9569,9588],{"className":9568},[1857],[1854,9570,9572],{"className":9571},[1861],[1863,9573,9574],{"xmlns":1865},[1867,9575,9576,9585],{},[1870,9577,9578,9580,9582],{},[1873,9579,1793],{},[1877,9581,1879],{},[1890,9583,9584],{},"0.05",[1913,9586,9587],{"encoding":1915},"p=0.05",[1854,9589,9591,9609],{"className":9590,"ariaHidden":1895},[1920],[1854,9592,9594,9597,9600,9603,9606],{"className":9593},[1924],[1854,9595],{"className":9596,"style":2425},[1928],[1854,9598,1793],{"className":9599},[1933,1934],[1854,9601],{"className":9602,"style":1940},[1939],[1854,9604,1879],{"className":9605},[1944],[1854,9607],{"className":9608,"style":1940},[1939],[1854,9610,9612,9615],{"className":9611},[1924],[1854,9613],{"className":9614,"style":9561},[1928],[1854,9616,9584],{"className":9617},[1933],"。这是 Wald 区间容易失败的场景。",[4933,9620],{"code64":9621,"layout":4936,"locale":7,"packages":9622,"title":9623},"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","numpy, scipy, matplotlib","Python：Wald 与 Wilson 覆盖率",[4940,9625],{"code64":9626,"layout":4936,"locale":7,"title":9627},"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","R：Wald 与 Wilson 覆盖率",[1793,9629,9630,9631,9659,9660,9688],{},"把 ",[1854,9632,9634,9647],{"className":9633},[1857],[1854,9635,9637],{"className":9636},[1861],[1863,9638,9639],{"xmlns":1865},[1867,9640,9641,9645],{},[1870,9642,9643],{},[1873,9644,1793],{},[1913,9646,1793],{"encoding":1915},[1854,9648,9650],{"className":9649,"ariaHidden":1895},[1920],[1854,9651,9653,9656],{"className":9652},[1924],[1854,9654],{"className":9655,"style":2425},[1928],[1854,9657,1793],{"className":9658},[1933,1934]," 改为 0.5，或把 ",[1854,9661,9663,9676],{"className":9662},[1857],[1854,9664,9666],{"className":9665},[1861],[1863,9667,9668],{"xmlns":1865},[1867,9669,9670,9674],{},[1870,9671,9672],{},[1873,9673,1908],{},[1913,9675,1908],{"encoding":1915},[1854,9677,9679],{"className":9678,"ariaHidden":1895},[1920],[1854,9680,9682,9685],{"className":9681},[1924],[1854,9683],{"className":9684,"style":2484},[1928],[1854,9686,1908],{"className":9687},[1933,1934]," 改为 300，观察大样本近似何时改善。",[1816,9690,9692],{"id":9691},"_6-渐近正态与-delta-方法","6. 渐近正态与 Delta 方法",[1793,9694,9695],{},"若",[1854,9697,9699],{"className":9698},[2118],[1854,9700,9702,9760],{"className":9701},[1857],[1854,9703,9705],{"className":9704},[1861],[1863,9706,9707],{"xmlns":1865,"display":2127},[1867,9708,9709,9757],{},[1870,9710,9711,9715,9717,9723,9725,9727,9729,9742,9744,9746,9748,9750,9753,9755],{},[3104,9712,9713],{},[1873,9714,1908],{},[1877,9716,1883],{"stretchy":1882},[2826,9718,9719,9721],{"accent":1895},[1873,9720,2096],{},[1877,9722,7053],{},[1877,9724,2294],{},[1873,9726,2096],{},[1877,9728,1911],{"stretchy":1882},[2826,9730,9731,9735],{},[1877,9732,9734],{"stretchy":1895,"minsize":9733},"3.0em","→",[9736,9737,9740],"mpadded",{"width":9738,"lspace":9739},"+0.6em","0.3em",[1873,9741,2841],{},[1873,9743,2844],{},[1877,9745,1883],{"stretchy":1882},[1890,9747,3116],{},[1877,9749,1896],{"separator":1895},[1873,9751,9752],{},"V",[1877,9754,1911],{"stretchy":1882},[1877,9756,1896],{"separator":1895},[1913,9758,9759],{"encoding":1915},"\\sqrt n(\\hat\\theta-\\theta)\n\\xrightarrow{d}N(0,V),",[1854,9761,9763,9862,9942],{"className":9762,"ariaHidden":1895},[1920],[1854,9764,9766,9770,9817,9820,9853,9856,9859],{"className":9765},[1924],[1854,9767],{"className":9768,"style":9769},[1928],"height:1.2079em;vertical-align:-0.25em;",[1854,9771,9773],{"className":9772},[1933,3195],[1854,9774,9776,9808],{"className":9775},[1972,1973],[1854,9777,9779,9805],{"className":9778},[1977],[1854,9780,9783,9792],{"className":9781,"style":9782},[1981],"height:0.8492em;",[1854,9784,9786,9789],{"className":9785,"style":2940},[3209],[1854,9787],{"className":9788,"style":2944},[1989],[1854,9790,1908],{"className":9791,"style":3216},[1933,1934],[1854,9793,9795,9798],{"style":9794},"top:-2.8092em;",[1854,9796],{"className":9797,"style":2944},[1989],[1854,9799,9801],{"className":9800,"style":3227},[3226],[3229,9802,9803],{"xmlns":3231,"width":3232,"height":3233,"viewBox":3234,"preserveAspectRatio":3235},[3237,9804],{"d":3239},[1854,9806,2005],{"className":9807},[2004],[1854,9809,9811],{"className":9810},[1977],[1854,9812,9815],{"className":9813,"style":9814},[1981],"height:0.1908em;",[1854,9816],{},[1854,9818,1883],{"className":9819},[1958],[1854,9821,9823],{"className":9822},[1933,3275],[1854,9824,9826],{"className":9825},[1972],[1854,9827,9829],{"className":9828},[1977],[1854,9830,9833,9841],{"className":9831,"style":9832},[1981],"height:0.9579em;",[1854,9834,9835,9838],{"style":2940},[1854,9836],{"className":9837,"style":2944},[1989],[1854,9839,2096],{"className":9840,"style":2113},[1933,1934],[1854,9842,9844,9847],{"style":9843},"top:-3.2634em;",[1854,9845],{"className":9846,"style":2944},[1989],[1854,9848,9850],{"className":9849,"style":3304},[3303],[1854,9851,7053],{"className":9852},[1933],[1854,9854],{"className":9855,"style":2411},[1939],[1854,9857,2294],{"className":9858},[2415],[1854,9860],{"className":9861,"style":2411},[1939],[1854,9863,9865,9869,9872,9875,9878,9939],{"className":9864},[1924],[1854,9866],{"className":9867,"style":9868},[1928],"height:1.3581em;vertical-align:-0.25em;",[1854,9870,2096],{"className":9871,"style":2113},[1933,1934],[1854,9873,1911],{"className":9874},[2080],[1854,9876],{"className":9877,"style":1940},[1939],[1854,9879,9882],{"className":9880},[1944,9881],"x-arrow",[1854,9883,9885,9930],{"className":9884},[1972,1973],[1854,9886,9888,9927],{"className":9887},[1977],[1854,9889,9892,9908],{"className":9890,"style":9891},[1981],"height:1.1081em;",[1854,9893,9895,9898],{"style":9894},"top:-3.322em;",[1854,9896],{"className":9897,"style":1990},[1989],[1854,9899,9902],{"className":9900},[1994,1995,1996,1997,9901],"x-arrow-pad",[1854,9903,9905],{"className":9904},[1933,1997],[1854,9906,2841],{"className":9907},[1933,1934,1997],[1854,9909,9912,9915],{"className":9910,"style":9911},[3209],"top:-2.689em;",[1854,9913],{"className":9914,"style":1990},[1989],[1854,9916,9919],{"className":9917,"style":9918},[3226],"height:0.522em;min-width:1.469em;",[3229,9920,9924],{"xmlns":3231,"width":3232,"height":9921,"viewBox":9922,"preserveAspectRatio":9923},"0.522em","0 0 400000 522","xMaxYMin slice",[3237,9925],{"d":9926},"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z",[1854,9928,2005],{"className":9929},[2004],[1854,9931,9933],{"className":9932},[1977],[1854,9934,9937],{"className":9935,"style":9936},[1981],"height:0.011em;",[1854,9938],{},[1854,9940],{"className":9941,"style":1940},[1939],[1854,9943,9945,9948,9951,9954,9957,9960,9963,9966,9969],{"className":9944},[1924],[1854,9946],{"className":9947,"style":1954},[1928],[1854,9949,2844],{"className":9950,"style":2233},[1933,1934],[1854,9952,1883],{"className":9953},[1958],[1854,9955,3116],{"className":9956},[1933],[1854,9958,1896],{"className":9959},[2018],[1854,9961],{"className":9962,"style":2022},[1939],[1854,9964,9752],{"className":9965,"style":2411},[1933,1934],[1854,9967,1911],{"className":9968},[2080],[1854,9970,1896],{"className":9971},[2018],[1793,9973,9974,9975,10102],{},"且有一致标准误估计 ",[1854,9976,9978,10010],{"className":9977},[1857],[1854,9979,9981],{"className":9980},[1861],[1863,9982,9983],{"xmlns":1865},[1867,9984,9985,10007],{},[1870,9986,9987,9997,9999,10005],{},[2826,9988,9989,9995],{"accent":1895},[1870,9990,9991,9993],{},[1873,9992,3955],{},[1873,9994,6989],{},[1877,9996,7053],{"stretchy":1895},[1877,9998,1883],{"stretchy":1882},[2826,10000,10001,10003],{"accent":1895},[1873,10002,2096],{},[1877,10004,7053],{},[1877,10006,1911],{"stretchy":1882},[1913,10008,10009],{"encoding":1915},"\\widehat{SE}(\\hat\\theta)",[1854,10011,10013],{"className":10012,"ariaHidden":1895},[1920],[1854,10014,10016,10020,10065,10068,10099],{"className":10015},[1924],[1854,10017],{"className":10018,"style":10019},[1928],"height:1.2333em;vertical-align:-0.25em;",[1854,10021,10023],{"className":10022},[1933,3275],[1854,10024,10026],{"className":10025},[1972],[1854,10027,10029],{"className":10028},[1977],[1854,10030,10033,10047],{"className":10031,"style":10032},[1981],"height:0.9833em;",[1854,10034,10035,10038],{"style":2940},[1854,10036],{"className":10037,"style":2944},[1989],[1854,10039,10041,10044],{"className":10040},[1933],[1854,10042,3955],{"className":10043,"style":3970},[1933,1934],[1854,10045,6989],{"className":10046,"style":3970},[1933,1934],[1854,10048,10051,10054],{"className":10049,"style":10050},[3209],"top:-3.6833em;",[1854,10052],{"className":10053,"style":2944},[1989],[1854,10055,10057],{"style":10056},"height:0.3em;",[3229,10058,10062],{"xmlns":3231,"width":10059,"height":9739,"viewBox":10060,"preserveAspectRatio":10061},"100%","0 0 2364 300","none",[3237,10063],{"d":10064},"M1181 0h2l1171 176c6 0 10 5 10 11l-2 23c-1 6-5 10\n-11 10h-1L1182 67 15 220h-1c-6 0-10-4-11-10l-2-23c-1-6 4-11 10-11z",[1854,10066,1883],{"className":10067},[1958],[1854,10069,10071],{"className":10070},[1933,3275],[1854,10072,10074],{"className":10073},[1972],[1854,10075,10077],{"className":10076},[1977],[1854,10078,10080,10088],{"className":10079,"style":9832},[1981],[1854,10081,10082,10085],{"style":2940},[1854,10083],{"className":10084,"style":2944},[1989],[1854,10086,2096],{"className":10087,"style":2113},[1933,1934],[1854,10089,10090,10093],{"style":9843},[1854,10091],{"className":10092,"style":2944},[1989],[1854,10094,10096],{"className":10095,"style":3304},[3303],[1854,10097,7053],{"className":10098},[1933],[1854,10100,1911],{"className":10101},[2080],"，Wald 区间为：",[1854,10104,10106],{"className":10105},[2118],[1854,10107,10109,10167],{"className":10108},[1857],[1854,10110,10112],{"className":10111},[1861],[1863,10113,10114],{"xmlns":1865,"display":2127},[1867,10115,10116,10164],{},[1870,10117,10118,10124,10126,10142,10152,10154,10160,10162],{},[2826,10119,10120,10122],{"accent":1895},[1873,10121,2096],{},[1877,10123,7053],{},[1877,10125,6134],{},[1885,10127,10128,10130],{},[1873,10129,3412],{},[1870,10131,10132,10134,10136,10138,10140],{},[1890,10133,1892],{},[1877,10135,2294],{},[1873,10137,2297],{},[1873,10139,3102],{"mathvariant":2525},[1890,10141,2860],{},[2826,10143,10144,10150],{"accent":1895},[1870,10145,10146,10148],{},[1873,10147,3955],{},[1873,10149,6989],{},[1877,10151,7053],{"stretchy":1895},[1877,10153,1883],{"stretchy":1882},[2826,10155,10156,10158],{"accent":1895},[1873,10157,2096],{},[1877,10159,7053],{},[1877,10161,1911],{"stretchy":1882},[1873,10163,3125],{"mathvariant":2525},[1913,10165,10166],{"encoding":1915},"\\hat\\theta\n\\pm z_{1-\\alpha\u002F2}\\widehat{SE}(\\hat\\theta).",[1854,10168,10170,10217],{"className":10169,"ariaHidden":1895},[1920],[1854,10171,10173,10177,10208,10211,10214],{"className":10172},[1924],[1854,10174],{"className":10175,"style":10176},[1928],"height:1.0412em;vertical-align:-0.0833em;",[1854,10178,10180],{"className":10179},[1933,3275],[1854,10181,10183],{"className":10182},[1972],[1854,10184,10186],{"className":10185},[1977],[1854,10187,10189,10197],{"className":10188,"style":9832},[1981],[1854,10190,10191,10194],{"style":2940},[1854,10192],{"className":10193,"style":2944},[1989],[1854,10195,2096],{"className":10196,"style":2113},[1933,1934],[1854,10198,10199,10202],{"style":9843},[1854,10200],{"className":10201,"style":2944},[1989],[1854,10203,10205],{"className":10204,"style":3304},[3303],[1854,10206,7053],{"className":10207},[1933],[1854,10209],{"className":10210,"style":2411},[1939],[1854,10212,6134],{"className":10213},[2415],[1854,10215],{"className":10216,"style":2411},[1939],[1854,10218,10220,10224,10276,10314,10317,10348,10351],{"className":10219},[1924],[1854,10221],{"className":10222,"style":10223},[1928],"height:1.3385em;vertical-align:-0.3552em;",[1854,10225,10227,10230],{"className":10226},[1933],[1854,10228,3412],{"className":10229,"style":3562},[1933,1934],[1854,10231,10233],{"className":10232},[1968],[1854,10234,10236,10268],{"className":10235},[1972,1973],[1854,10237,10239,10265],{"className":10238},[1977],[1854,10240,10242],{"className":10241,"style":3575},[1981],[1854,10243,10244,10247],{"style":3578},[1854,10245],{"className":10246,"style":1990},[1989],[1854,10248,10250],{"className":10249},[1994,1995,1996,1997],[1854,10251,10253,10256,10259,10262],{"className":10252},[1933,1997],[1854,10254,1892],{"className":10255},[1933,1997],[1854,10257,2294],{"className":10258},[2415,1997],[1854,10260,2297],{"className":10261,"style":2429},[1933,1934,1997],[1854,10263,3600],{"className":10264},[1933,1997],[1854,10266,2005],{"className":10267},[2004],[1854,10269,10271],{"className":10270},[1977],[1854,10272,10274],{"className":10273,"style":3610},[1981],[1854,10275],{},[1854,10277,10279],{"className":10278},[1933,3275],[1854,10280,10282],{"className":10281},[1972],[1854,10283,10285],{"className":10284},[1977],[1854,10286,10288,10302],{"className":10287,"style":10032},[1981],[1854,10289,10290,10293],{"style":2940},[1854,10291],{"className":10292,"style":2944},[1989],[1854,10294,10296,10299],{"className":10295},[1933],[1854,10297,3955],{"className":10298,"style":3970},[1933,1934],[1854,10300,6989],{"className":10301,"style":3970},[1933,1934],[1854,10303,10305,10308],{"className":10304,"style":10050},[3209],[1854,10306],{"className":10307,"style":2944},[1989],[1854,10309,10310],{"style":10056},[3229,10311,10312],{"xmlns":3231,"width":10059,"height":9739,"viewBox":10060,"preserveAspectRatio":10061},[3237,10313],{"d":10064},[1854,10315,1883],{"className":10316},[1958],[1854,10318,10320],{"className":10319},[1933,3275],[1854,10321,10323],{"className":10322},[1972],[1854,10324,10326],{"className":10325},[1977],[1854,10327,10329,10337],{"className":10328,"style":9832},[1981],[1854,10330,10331,10334],{"style":2940},[1854,10332],{"className":10333,"style":2944},[1989],[1854,10335,2096],{"className":10336,"style":2113},[1933,1934],[1854,10338,10339,10342],{"style":9843},[1854,10340],{"className":10341,"style":2944},[1989],[1854,10343,10345],{"className":10344,"style":3304},[3303],[1854,10346,7053],{"className":10347},[1933],[1854,10349,1911],{"className":10350},[2080],[1854,10352,3125],{"className":10353},[1933],[1793,10355,10356,10357,10402],{},"对变换参数 ",[1854,10358,10360,10381],{"className":10359},[1857],[1854,10361,10363],{"className":10362},[1861],[1863,10364,10365],{"xmlns":1865},[1867,10366,10367,10378],{},[1870,10368,10369,10372,10374,10376],{},[1873,10370,10371],{},"g",[1877,10373,1883],{"stretchy":1882},[1873,10375,2096],{},[1877,10377,1911],{"stretchy":1882},[1913,10379,10380],{"encoding":1915},"g(\\theta)",[1854,10382,10384],{"className":10383,"ariaHidden":1895},[1920],[1854,10385,10387,10390,10393,10396,10399],{"className":10386},[1924],[1854,10388],{"className":10389,"style":1954},[1928],[1854,10391,10371],{"className":10392,"style":3000},[1933,1934],[1854,10394,1883],{"className":10395},[1958],[1854,10397,2096],{"className":10398,"style":2113},[1933,1934],[1854,10400,1911],{"className":10401},[2080],"，Delta 方法给出：",[1854,10404,10406],{"className":10405},[2118],[1854,10407,10409,10497],{"className":10408},[1857],[1854,10410,10412],{"className":10411},[1861],[1863,10413,10414],{"xmlns":1865,"display":2127},[1867,10415,10416,10494],{},[1870,10417,10418,10422,10424,10426,10428,10434,10436,10438,10440,10442,10444,10446,10448,10456,10458,10492],{},[3104,10419,10420],{},[1873,10421,1908],{},[1877,10423,2271],{"stretchy":1882},[1873,10425,10371],{},[1877,10427,1883],{"stretchy":1882},[2826,10429,10430,10432],{"accent":1895},[1873,10431,2096],{},[1877,10433,7053],{},[1877,10435,1911],{"stretchy":1882},[1877,10437,2294],{},[1873,10439,10371],{},[1877,10441,1883],{"stretchy":1882},[1873,10443,2096],{},[1877,10445,1911],{"stretchy":1882},[1877,10447,2287],{"stretchy":1882},[2826,10449,10450,10452],{},[1877,10451,9734],{"stretchy":1895,"minsize":9733},[9736,10453,10454],{"width":9738,"lspace":9739},[1873,10455,2841],{},[1873,10457,2844],{},[1870,10459,10460,10462,10464,10466,10468,10476,10478,10480,10482,10488,10490],{},[1877,10461,1883],{"fence":1895},[1890,10463,3116],{},[1877,10465,1896],{"separator":1895},[1877,10467,2145],{"stretchy":1882},[2853,10469,10470,10472],{},[1873,10471,10371],{},[1877,10473,10475],{"mathvariant":2525,"lspace":10474,"rspace":10474},"0em","′",[1877,10477,1883],{"stretchy":1882},[1873,10479,2096],{},[1877,10481,1911],{"stretchy":1882},[2853,10483,10484,10486],{},[1877,10485,2168],{"stretchy":1882},[1890,10487,2860],{},[1873,10489,9752],{},[1877,10491,1911],{"fence":1895},[1873,10493,3125],{"mathvariant":2525},[1913,10495,10496],{"encoding":1915},"\\sqrt n\\{g(\\hat\\theta)-g(\\theta)\\}\n\\xrightarrow{d}\nN\\left(0,[g'(\\theta)]^2V\\right).",[1854,10498,10500,10602,10676],{"className":10499,"ariaHidden":1895},[1920],[1854,10501,10503,10506,10550,10553,10556,10559,10590,10593,10596,10599],{"className":10502},[1924],[1854,10504],{"className":10505,"style":9769},[1928],[1854,10507,10509],{"className":10508},[1933,3195],[1854,10510,10512,10542],{"className":10511},[1972,1973],[1854,10513,10515,10539],{"className":10514},[1977],[1854,10516,10518,10527],{"className":10517,"style":9782},[1981],[1854,10519,10521,10524],{"className":10520,"style":2940},[3209],[1854,10522],{"className":10523,"style":2944},[1989],[1854,10525,1908],{"className":10526,"style":3216},[1933,1934],[1854,10528,10529,10532],{"style":9794},[1854,10530],{"className":10531,"style":2944},[1989],[1854,10533,10535],{"className":10534,"style":3227},[3226],[3229,10536,10537],{"xmlns":3231,"width":3232,"height":3233,"viewBox":3234,"preserveAspectRatio":3235},[3237,10538],{"d":3239},[1854,10540,2005],{"className":10541},[2004],[1854,10543,10545],{"className":10544},[1977],[1854,10546,10548],{"className":10547,"style":9814},[1981],[1854,10549],{},[1854,10551,2271],{"className":10552},[1958],[1854,10554,10371],{"className":10555,"style":3000},[1933,1934],[1854,10557,1883],{"className":10558},[1958],[1854,10560,10562],{"className":10561},[1933,3275],[1854,10563,10565],{"className":10564},[1972],[1854,10566,10568],{"className":10567},[1977],[1854,10569,10571,10579],{"className":10570,"style":9832},[1981],[1854,10572,10573,10576],{"style":2940},[1854,10574],{"className":10575,"style":2944},[1989],[1854,10577,2096],{"className":10578,"style":2113},[1933,1934],[1854,10580,10581,10584],{"style":9843},[1854,10582],{"className":10583,"style":2944},[1989],[1854,10585,10587],{"className":10586,"style":3304},[3303],[1854,10588,7053],{"className":10589},[1933],[1854,10591,1911],{"className":10592},[2080],[1854,10594],{"className":10595,"style":2411},[1939],[1854,10597,2294],{"className":10598},[2415],[1854,10600],{"className":10601,"style":2411},[1939],[1854,10603,10605,10608,10611,10614,10617,10620,10623,10673],{"className":10604},[1924],[1854,10606],{"className":10607,"style":9868},[1928],[1854,10609,10371],{"className":10610,"style":3000},[1933,1934],[1854,10612,1883],{"className":10613},[1958],[1854,10615,2096],{"className":10616,"style":2113},[1933,1934],[1854,10618,2388],{"className":10619},[2080],[1854,10621],{"className":10622,"style":1940},[1939],[1854,10624,10626],{"className":10625},[1944,9881],[1854,10627,10629,10665],{"className":10628},[1972,1973],[1854,10630,10632,10662],{"className":10631},[1977],[1854,10633,10635,10649],{"className":10634,"style":9891},[1981],[1854,10636,10637,10640],{"style":9894},[1854,10638],{"className":10639,"style":1990},[1989],[1854,10641,10643],{"className":10642},[1994,1995,1996,1997,9901],[1854,10644,10646],{"className":10645},[1933,1997],[1854,10647,2841],{"className":10648},[1933,1934,1997],[1854,10650,10652,10655],{"className":10651,"style":9911},[3209],[1854,10653],{"className":10654,"style":1990},[1989],[1854,10656,10658],{"className":10657,"style":9918},[3226],[3229,10659,10660],{"xmlns":3231,"width":3232,"height":9921,"viewBox":9922,"preserveAspectRatio":9923},[3237,10661],{"d":9926},[1854,10663,2005],{"className":10664},[2004],[1854,10666,10668],{"className":10667},[1977],[1854,10669,10671],{"className":10670,"style":9936},[1981],[1854,10672],{},[1854,10674],{"className":10675,"style":1940},[1939],[1854,10677,10679,10683,10686,10689,10791,10794],{"className":10678},[1924],[1854,10680],{"className":10681,"style":10682},[1928],"height:1.2141em;vertical-align:-0.35em;",[1854,10684,2844],{"className":10685,"style":2233},[1933,1934],[1854,10687],{"className":10688,"style":2022},[1939],[1854,10690,10692,10699,10702,10705,10708,10711,10744,10747,10750,10753,10782,10785],{"className":10691},[2026],[1854,10693,10695],{"className":10694,"style":3511},[1958,3510],[1854,10696,1883],{"className":10697},[3515,10698],"size1",[1854,10700,3116],{"className":10701},[1933],[1854,10703,1896],{"className":10704},[2018],[1854,10706],{"className":10707,"style":2022},[1939],[1854,10709,2145],{"className":10710},[1958],[1854,10712,10714,10717],{"className":10713},[1933],[1854,10715,10371],{"className":10716,"style":3000},[1933,1934],[1854,10718,10720],{"className":10719},[1968],[1854,10721,10723],{"className":10722},[1972],[1854,10724,10726],{"className":10725},[1977],[1854,10727,10730],{"className":10728,"style":10729},[1981],"height:0.8019em;",[1854,10731,10732,10735],{"style":5428},[1854,10733],{"className":10734,"style":1990},[1989],[1854,10736,10738],{"className":10737},[1994,1995,1996,1997],[1854,10739,10741],{"className":10740},[1933,1997],[1854,10742,10475],{"className":10743},[1933,1997],[1854,10745,1883],{"className":10746},[1958],[1854,10748,2096],{"className":10749,"style":2113},[1933,1934],[1854,10751,1911],{"className":10752},[2080],[1854,10754,10756,10759],{"className":10755},[2080],[1854,10757,2168],{"className":10758},[2080],[1854,10760,10762],{"className":10761},[1968],[1854,10763,10765],{"className":10764},[1972],[1854,10766,10768],{"className":10767},[1977],[1854,10769,10771],{"className":10770,"style":5404},[1981],[1854,10772,10773,10776],{"style":5428},[1854,10774],{"className":10775,"style":1990},[1989],[1854,10777,10779],{"className":10778},[1994,1995,1996,1997],[1854,10780,2860],{"className":10781},[1933,1997],[1854,10783,9752],{"className":10784,"style":2411},[1933,1934],[1854,10786,10788],{"className":10787,"style":3511},[2080,3510],[1854,10789,1911],{"className":10790},[3515,10698],[1854,10792],{"className":10793,"style":2022},[1939],[1854,10795,3125],{"className":10796},[1933],[1793,10798,10799,10800,10853,10854,10899],{},"例如估计正参数 ",[1854,10801,10803,10822],{"className":10802},[1857],[1854,10804,10806],{"className":10805},[1861],[1863,10807,10808],{"xmlns":1865},[1867,10809,10810,10819],{},[1870,10811,10812,10814,10817],{},[1873,10813,2096],{},[1877,10815,10816],{},">",[1890,10818,3116],{},[1913,10820,10821],{"encoding":1915},"\\theta>0",[1854,10823,10825,10844],{"className":10824,"ariaHidden":1895},[1920],[1854,10826,10828,10832,10835,10838,10841],{"className":10827},[1924],[1854,10829],{"className":10830,"style":10831},[1928],"height:0.7335em;vertical-align:-0.0391em;",[1854,10833,2096],{"className":10834,"style":2113},[1933,1934],[1854,10836],{"className":10837,"style":1940},[1939],[1854,10839,10816],{"className":10840},[1944],[1854,10842],{"className":10843,"style":1940},[1939],[1854,10845,10847,10850],{"className":10846},[1924],[1854,10848],{"className":10849,"style":9561},[1928],[1854,10851,3116],{"className":10852},[1933]," 时，可先对 ",[1854,10855,10857,10877],{"className":10856},[1857],[1854,10858,10860],{"className":10859},[1861],[1863,10861,10862],{"xmlns":1865},[1867,10863,10864,10874],{},[1870,10865,10866,10869,10872],{},[1873,10867,10868],{},"log",[1877,10870,10871],{},"⁡",[1873,10873,2096],{},[1913,10875,10876],{"encoding":1915},"\\log\\theta",[1854,10878,10880],{"className":10879,"ariaHidden":1895},[1920],[1854,10881,10883,10886,10893,10896],{"className":10882},[1924],[1854,10884],{"className":10885,"style":8127},[1928],[1854,10887,10889,10890],{"className":10888},[2926],"lo",[1854,10891,10371],{"style":10892},"margin-right:0.0139em;",[1854,10894],{"className":10895,"style":2022},[1939],[1854,10897,2096],{"className":10898,"style":2113},[1933,1934]," 构造对称区间，再指数变换回原尺度，保证端点为正。与直接在原尺度使用 Wald 区间相比，这常更符合参数边界和分布偏斜。",[1816,10901,10903],{"id":10902},"_7-似然区间","7. 似然区间",[1793,10905,2803,10906,10951],{},[1854,10907,10909,10930],{"className":10908},[1857],[1854,10910,10912],{"className":10911},[1861],[1863,10913,10914],{"xmlns":1865},[1867,10915,10916,10927],{},[1870,10917,10918,10921,10923,10925],{},[1873,10919,10920],{"mathvariant":2525},"ℓ",[1877,10922,1883],{"stretchy":1882},[1873,10924,2096],{},[1877,10926,1911],{"stretchy":1882},[1913,10928,10929],{"encoding":1915},"\\ell(\\theta)",[1854,10931,10933],{"className":10932,"ariaHidden":1895},[1920],[1854,10934,10936,10939,10942,10945,10948],{"className":10935},[1924],[1854,10937],{"className":10938,"style":1954},[1928],[1854,10940,10920],{"className":10941},[1933],[1854,10943,1883],{"className":10944},[1958],[1854,10946,2096],{"className":10947,"style":2113},[1933,1934],[1854,10949,1911],{"className":10950},[2080]," 是对数似然，似然比区间可写为：",[1854,10953,10955],{"className":10954},[2118],[1854,10956,10958,11020],{"className":10957},[1857],[1854,10959,10961],{"className":10960},[1861],[1863,10962,10963],{"xmlns":1865,"display":2127},[1867,10964,10965,11017],{},[1870,10966,10967,10969,10971,10973,10975,10981,10983,10985,10987,10989,10991,10993,10995,10997,11015],{},[1890,10968,2860],{},[1877,10970,2271],{"stretchy":1882},[1873,10972,10920],{"mathvariant":2525},[1877,10974,1883],{"stretchy":1882},[2826,10976,10977,10979],{"accent":1895},[1873,10978,2096],{},[1877,10980,7053],{},[1877,10982,1911],{"stretchy":1882},[1877,10984,2294],{},[1873,10986,10920],{"mathvariant":2525},[1877,10988,1883],{"stretchy":1882},[1873,10990,2096],{},[1877,10992,1911],{"stretchy":1882},[1877,10994,2287],{"stretchy":1882},[1877,10996,2616],{},[5200,10998,10999,11001,11013],{},[1873,11000,5204],{},[1870,11002,11003,11005,11007,11009,11011],{},[1890,11004,1892],{},[1877,11006,1896],{"separator":1895},[1890,11008,1892],{},[1877,11010,2294],{},[1873,11012,2297],{},[1890,11014,2860],{},[1873,11016,3125],{"mathvariant":2525},[1913,11018,11019],{"encoding":1915},"2\\{\\ell(\\hat\\theta)-\\ell(\\theta)\\}\n\\le \\chi^2_{1,1-\\alpha}.",[1854,11021,11023,11084,11111],{"className":11022,"ariaHidden":1895},[1920],[1854,11024,11026,11029,11032,11035,11038,11041,11072,11075,11078,11081],{"className":11025},[1924],[1854,11027],{"className":11028,"style":9769},[1928],[1854,11030,2860],{"className":11031},[1933],[1854,11033,2271],{"className":11034},[1958],[1854,11036,10920],{"className":11037},[1933],[1854,11039,1883],{"className":11040},[1958],[1854,11042,11044],{"className":11043},[1933,3275],[1854,11045,11047],{"className":11046},[1972],[1854,11048,11050],{"className":11049},[1977],[1854,11051,11053,11061],{"className":11052,"style":9832},[1981],[1854,11054,11055,11058],{"style":2940},[1854,11056],{"className":11057,"style":2944},[1989],[1854,11059,2096],{"className":11060,"style":2113},[1933,1934],[1854,11062,11063,11066],{"style":9843},[1854,11064],{"className":11065,"style":2944},[1989],[1854,11067,11069],{"className":11068,"style":3304},[3303],[1854,11070,7053],{"className":11071},[1933],[1854,11073,1911],{"className":11074},[2080],[1854,11076],{"className":11077,"style":2411},[1939],[1854,11079,2294],{"className":11080},[2415],[1854,11082],{"className":11083,"style":2411},[1939],[1854,11085,11087,11090,11093,11096,11099,11102,11105,11108],{"className":11086},[1924],[1854,11088],{"className":11089,"style":1954},[1928],[1854,11091,10920],{"className":11092},[1933],[1854,11094,1883],{"className":11095},[1958],[1854,11097,2096],{"className":11098,"style":2113},[1933,1934],[1854,11100,2388],{"className":11101},[2080],[1854,11103],{"className":11104,"style":1940},[1939],[1854,11106,2616],{"className":11107},[1944],[1854,11109],{"className":11110,"style":1940},[1939],[1854,11112,11114,11118,11185],{"className":11113},[1924],[1854,11115],{"className":11116,"style":11117},[1928],"height:1.2472em;vertical-align:-0.3831em;",[1854,11119,11121,11124],{"className":11120},[1933],[1854,11122,5204],{"className":11123},[1933,1934],[1854,11125,11127],{"className":11126},[1968],[1854,11128,11130,11176],{"className":11129},[1972,1973],[1854,11131,11133,11173],{"className":11132},[1977],[1854,11134,11136,11162],{"className":11135,"style":5404},[1981],[1854,11137,11138,11141],{"style":5407},[1854,11139],{"className":11140,"style":1990},[1989],[1854,11142,11144],{"className":11143},[1994,1995,1996,1997],[1854,11145,11147,11150,11153,11156,11159],{"className":11146},[1933,1997],[1854,11148,1892],{"className":11149},[1933,1997],[1854,11151,1896],{"className":11152},[2018,1997],[1854,11154,1892],{"className":11155},[1933,1997],[1854,11157,2294],{"className":11158},[2415,1997],[1854,11160,2297],{"className":11161,"style":2429},[1933,1934,1997],[1854,11163,11164,11167],{"style":5428},[1854,11165],{"className":11166,"style":1990},[1989],[1854,11168,11170],{"className":11169},[1994,1995,1996,1997],[1854,11171,2860],{"className":11172},[1933,1997],[1854,11174,2005],{"className":11175},[2004],[1854,11177,11179],{"className":11178},[1977],[1854,11180,11183],{"className":11181,"style":11182},[1981],"height:0.3831em;",[1854,11184],{},[1854,11186,3125],{"className":11187},[1933],[1793,11189,11190],{},"它保留似然曲面的不对称性，在参数接近边界或似然明显偏斜时可能优于对称 Wald 区间。代价是需要对候选参数重复计算或优化似然。",[1793,11192,11193],{},"Score、Wald 和 likelihood-ratio 三类区间在正则大样本下渐近等价，但有限样本表现可能不同。",[1816,11195,11197],{"id":11196},"_8-bootstrap-区间","8. Bootstrap 区间",[1793,11199,11200],{},"Bootstrap 通过重抽样近似估计量的抽样分布。常见区间包括：",[11202,11203,11204,11220],"table",{},[11205,11206,11207],"thead",{},[11208,11209,11210,11214,11217],"tr",{},[11211,11212,11213],"th",{},"方法",[11211,11215,11216],{},"构造",[11211,11218,11219],{},"主要特点",[11221,11222,11223,11433,11444,11738,11749],"tbody",{},[11208,11224,11225,11229,11430],{},[11226,11227,11228],"td",{},"正态近似",[11226,11230,11231],{},[1854,11232,11234,11282],{"className":11233},[1857],[1854,11235,11237],{"className":11236},[1861],[1863,11238,11239],{"xmlns":1865},[1867,11240,11241,11279],{},[1870,11242,11243,11249,11251,11253,11256],{},[2826,11244,11245,11247],{"accent":1895},[1873,11246,2096],{},[1877,11248,7053],{},[1877,11250,6134],{},[1873,11252,3412],{},[8646,11254,11255],{}," ",[1885,11257,11258,11268],{},[2826,11259,11260,11266],{"accent":1895},[1870,11261,11262,11264],{},[1873,11263,3955],{},[1873,11265,6989],{},[1877,11267,7053],{"stretchy":1895},[1870,11269,11270,11272,11275,11277],{},[1873,11271,2634],{},[1873,11273,11274],{},"o",[1873,11276,11274],{},[1873,11278,4051],{},[1913,11280,11281],{"encoding":1915},"\\hat\\theta\\pm z\\,\\widehat{SE}_{boot}",[1854,11283,11285,11331],{"className":11284,"ariaHidden":1895},[1920],[1854,11286,11288,11291,11322,11325,11328],{"className":11287},[1924],[1854,11289],{"className":11290,"style":10176},[1928],[1854,11292,11294],{"className":11293},[1933,3275],[1854,11295,11297],{"className":11296},[1972],[1854,11298,11300],{"className":11299},[1977],[1854,11301,11303,11311],{"className":11302,"style":9832},[1981],[1854,11304,11305,11308],{"style":2940},[1854,11306],{"className":11307,"style":2944},[1989],[1854,11309,2096],{"className":11310,"style":2113},[1933,1934],[1854,11312,11313,11316],{"style":9843},[1854,11314],{"className":11315,"style":2944},[1989],[1854,11317,11319],{"className":11318,"style":3304},[3303],[1854,11320,7053],{"className":11321},[1933],[1854,11323],{"className":11324,"style":2411},[1939],[1854,11326,6134],{"className":11327},[2415],[1854,11329],{"className":11330,"style":2411},[1939],[1854,11332,11334,11338,11341,11344],{"className":11333},[1924],[1854,11335],{"className":11336,"style":11337},[1928],"height:1.1333em;vertical-align:-0.15em;",[1854,11339,3412],{"className":11340,"style":3562},[1933,1934],[1854,11342],{"className":11343,"style":2022},[1939],[1854,11345,11347,11385],{"className":11346},[1933],[1854,11348,11350],{"className":11349},[1933,3275],[1854,11351,11353],{"className":11352},[1972],[1854,11354,11356],{"className":11355},[1977],[1854,11357,11359,11373],{"className":11358,"style":10032},[1981],[1854,11360,11361,11364],{"style":2940},[1854,11362],{"className":11363,"style":2944},[1989],[1854,11365,11367,11370],{"className":11366},[1933],[1854,11368,3955],{"className":11369,"style":3970},[1933,1934],[1854,11371,6989],{"className":11372,"style":3970},[1933,1934],[1854,11374,11376,11379],{"className":11375,"style":10050},[3209],[1854,11377],{"className":11378,"style":2944},[1989],[1854,11380,11381],{"style":10056},[3229,11382,11383],{"xmlns":3231,"width":10059,"height":9739,"viewBox":10060,"preserveAspectRatio":10061},[3237,11384],{"d":10064},[1854,11386,11388],{"className":11387},[1968],[1854,11389,11391,11422],{"className":11390},[1972,1973],[1854,11392,11394,11419],{"className":11393},[1977],[1854,11395,11397],{"className":11396,"style":2331},[1981],[1854,11398,11400,11403],{"style":11399},"top:-2.55em;margin-right:0.05em;",[1854,11401],{"className":11402,"style":1990},[1989],[1854,11404,11406],{"className":11405},[1994,1995,1996,1997],[1854,11407,11409,11412,11416],{"className":11408},[1933,1997],[1854,11410,2634],{"className":11411},[1933,1934,1997],[1854,11413,11415],{"className":11414},[1933,1934,1997],"oo",[1854,11417,4051],{"className":11418},[1933,1934,1997],[1854,11420,2005],{"className":11421},[2004],[1854,11423,11425],{"className":11424},[1977],[1854,11426,11428],{"className":11427,"style":2012},[1981],[1854,11429],{},[11226,11431,11432],{},"简单，但忽略偏斜",[11208,11434,11435,11438,11441],{},[11226,11436,11437],{},"百分位",[11226,11439,11440],{},"Bootstrap 分布的分位数",[11226,11442,11443],{},"直观、变换不变",[11208,11445,11446,11449,11735],{},[11226,11447,11448],{},"Basic",[11226,11450,11451],{},[1854,11452,11454,11519],{"className":11453},[1857],[1854,11455,11457],{"className":11456},[1861],[1863,11458,11459],{"xmlns":1865},[1867,11460,11461,11516],{},[1870,11462,11463,11465,11471,11473,11490,11492,11494,11496,11502,11504],{},[1890,11464,2860],{},[2826,11466,11467,11469],{"accent":1895},[1873,11468,2096],{},[1877,11470,7053],{},[1877,11472,2294],{},[1885,11474,11475,11478],{},[1873,11476,11477],{},"q",[1870,11479,11480,11482,11484,11486,11488],{},[1890,11481,1892],{},[1877,11483,2294],{},[1873,11485,2297],{},[1873,11487,3102],{"mathvariant":2525},[1890,11489,2860],{},[1877,11491,1896],{"separator":1895},[8646,11493,11255],{},[1890,11495,2860],{},[2826,11497,11498,11500],{"accent":1895},[1873,11499,2096],{},[1877,11501,7053],{},[1877,11503,2294],{},[1885,11505,11506,11508],{},[1873,11507,11477],{},[1870,11509,11510,11512,11514],{},[1873,11511,2297],{},[1873,11513,3102],{"mathvariant":2525},[1890,11515,2860],{},[1913,11517,11518],{"encoding":1915},"2\\hat\\theta-q_{1-\\alpha\u002F2},\\,2\\hat\\theta-q_{\\alpha\u002F2}",[1854,11520,11522,11571,11683],{"className":11521,"ariaHidden":1895},[1920],[1854,11523,11525,11528,11531,11562,11565,11568],{"className":11524},[1924],[1854,11526],{"className":11527,"style":10176},[1928],[1854,11529,2860],{"className":11530},[1933],[1854,11532,11534],{"className":11533},[1933,3275],[1854,11535,11537],{"className":11536},[1972],[1854,11538,11540],{"className":11539},[1977],[1854,11541,11543,11551],{"className":11542,"style":9832},[1981],[1854,11544,11545,11548],{"style":2940},[1854,11546],{"className":11547,"style":2944},[1989],[1854,11549,2096],{"className":11550,"style":2113},[1933,1934],[1854,11552,11553,11556],{"style":9843},[1854,11554],{"className":11555,"style":2944},[1989],[1854,11557,11559],{"className":11558,"style":3304},[3303],[1854,11560,7053],{"className":11561},[1933],[1854,11563],{"className":11564,"style":2411},[1939],[1854,11566,2294],{"className":11567},[2415],[1854,11569],{"className":11570,"style":2411},[1939],[1854,11572,11574,11578,11631,11634,11637,11640,11643,11674,11677,11680],{"className":11573},[1924],[1854,11575],{"className":11576,"style":11577},[1928],"height:1.3131em;vertical-align:-0.3552em;",[1854,11579,11581,11584],{"className":11580},[1933],[1854,11582,11477],{"className":11583,"style":3000},[1933,1934],[1854,11585,11587],{"className":11586},[1968],[1854,11588,11590,11623],{"className":11589},[1972,1973],[1854,11591,11593,11620],{"className":11592},[1977],[1854,11594,11596],{"className":11595,"style":3575},[1981],[1854,11597,11599,11602],{"style":11598},"top:-2.5198em;margin-left:-0.0359em;margin-right:0.05em;",[1854,11600],{"className":11601,"style":1990},[1989],[1854,11603,11605],{"className":11604},[1994,1995,1996,1997],[1854,11606,11608,11611,11614,11617],{"className":11607},[1933,1997],[1854,11609,1892],{"className":11610},[1933,1997],[1854,11612,2294],{"className":11613},[2415,1997],[1854,11615,2297],{"className":11616,"style":2429},[1933,1934,1997],[1854,11618,3600],{"className":11619},[1933,1997],[1854,11621,2005],{"className":11622},[2004],[1854,11624,11626],{"className":11625},[1977],[1854,11627,11629],{"className":11628,"style":3610},[1981],[1854,11630],{},[1854,11632,1896],{"className":11633},[2018],[1854,11635],{"className":11636,"style":2022},[1939],[1854,11638],{"className":11639,"style":2022},[1939],[1854,11641,2860],{"className":11642},[1933],[1854,11644,11646],{"className":11645},[1933,3275],[1854,11647,11649],{"className":11648},[1972],[1854,11650,11652],{"className":11651},[1977],[1854,11653,11655,11663],{"className":11654,"style":9832},[1981],[1854,11656,11657,11660],{"style":2940},[1854,11658],{"className":11659,"style":2944},[1989],[1854,11661,2096],{"className":11662,"style":2113},[1933,1934],[1854,11664,11665,11668],{"style":9843},[1854,11666],{"className":11667,"style":2944},[1989],[1854,11669,11671],{"className":11670,"style":3304},[3303],[1854,11672,7053],{"className":11673},[1933],[1854,11675],{"className":11676,"style":2411},[1939],[1854,11678,2294],{"className":11679},[2415],[1854,11681],{"className":11682,"style":2411},[1939],[1854,11684,11686,11689],{"className":11685},[1924],[1854,11687],{"className":11688,"style":8576},[1928],[1854,11690,11692,11695],{"className":11691},[1933],[1854,11693,11477],{"className":11694,"style":3000},[1933,1934],[1854,11696,11698],{"className":11697},[1968],[1854,11699,11701,11727],{"className":11700},[1972,1973],[1854,11702,11704,11724],{"className":11703},[1977],[1854,11705,11707],{"className":11706,"style":3575},[1981],[1854,11708,11709,11712],{"style":11598},[1854,11710],{"className":11711,"style":1990},[1989],[1854,11713,11715],{"className":11714},[1994,1995,1996,1997],[1854,11716,11718,11721],{"className":11717},[1933,1997],[1854,11719,2297],{"className":11720,"style":2429},[1933,1934,1997],[1854,11722,3600],{"className":11723},[1933,19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Bootstrap 偏差",[11208,11739,11740,11743,11746],{},[11226,11741,11742],{},"BCa",[11226,11744,11745],{},"校正偏差与加速度",[11226,11747,11748],{},"精度更高，计算更复杂",[11208,11750,11751,11754,11757],{},[11226,11752,11753],{},"Studentized",[11226,11755,11756],{},"对标准化统计量重抽样",[11226,11758,11759],{},"理论性质好，常需嵌套计算",[2797,11761,11763],{"id":11762},"偏斜分布中位数的-bootstrap-区间","偏斜分布中位数的 Bootstrap 区间",[1793,11765,11766],{},"中位数的有限样本标准误公式不如均值直接。下面对指数分布样本使用百分位 Bootstrap。",[4933,11768],{"code64":11769,"layout":4936,"locale":7,"packages":11770,"title":11771},"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","numpy, matplotlib","Python：中位数的 Bootstrap 区间",[4940,11773],{"code64":11774,"layout":4936,"locale":7,"title":11775},"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","R：中位数的 Bootstrap 区间",[1793,11777,11778],{},"Bootstrap 仍要求重抽样方案模拟真实抽样机制。时间序列应保留时间依赖，分层抽样应按设计重抽样，聚类数据通常按群组重抽样。",[1816,11780,11782],{"id":11781},"_9-覆盖率长度与样本量的权衡","9. 覆盖率、长度与样本量的权衡",[1793,11784,11785],{},"区间评价至少包含三个维度：",[1823,11787,11788,11794,11800],{},[1800,11789,11790,11793],{},[2588,11791,11792],{},"覆盖率","：实际覆盖是否接近标称水平？",[1800,11795,11796,11799],{},[2588,11797,11798],{},"平均长度","：在覆盖可靠时是否足够精确？",[1800,11801,11802,11805],{},[2588,11803,11804],{},"稳定性","：端点是否受极端值、边界或数值优化强烈影响？",[1793,11807,11808,11809,11837],{},"提高置信水平会增加覆盖率但加宽区间；增加样本量通常缩短区间。若希望均值区间半宽不超过 ",[1854,11810,11812,11825],{"className":11811},[1857],[1854,11813,11815],{"className":11814},[1861],[1863,11816,11817],{"xmlns":1865},[1867,11818,11819,11823],{},[1870,11820,11821],{},[1873,11822,6989],{},[1913,11824,6989],{"encoding":1915},[1854,11826,11828],{"className":11827,"ariaHidden":1895},[1920],[1854,11829,11831,11834],{"className":11830},[1924],[1854,11832],{"className":11833,"style":1929},[1928],[1854,11835,6989],{"className":11836,"style":3970},[1933,1934],"，方差已知的粗略样本量为：",[1854,11839,11841],{"className":11840},[2118],[1854,11842,11844,11897],{"className":11843},[1857],[1854,11845,11847],{"className":11846},[1861],[1863,11848,11849],{"xmlns":1865,"display":2127},[1867,11850,11851,11894],{},[1870,11852,11853,11855,11858,11892],{},[1873,11854,1908],{},[1877,11856,11857],{},"≥",[2853,11859,11860,11890],{},[1870,11861,11862,11864,11888],{},[1877,11863,1883],{"fence":1895},[3081,11865,11866,11886],{},[1870,11867,11868,11884],{},[1885,11869,11870,11872],{},[1873,11871,3412],{},[1870,11873,11874,11876,11878,11880,11882],{},[1890,11875,1892],{},[1877,11877,2294],{},[1873,11879,2297],{},[1873,11881,3102],{"mathvariant":2525},[1890,11883,2860],{},[1873,11885,2857],{},[1873,11887,6989],{},[1877,11889,1911],{"fence":1895},[1890,11891,2860],{},[1873,11893,3125],{"mathvariant":2525},[1913,11895,11896],{"encoding":1915},"n\\ge\n\\left(\\frac{z_{1-\\alpha\u002F2}\\sigma}{E}\\right)^2.",[1854,11898,11900,11919],{"className":11899,"ariaHidden":1895},[1920],[1854,11901,11903,11907,11910,11913,11916],{"className":11902},[1924],[1854,11904],{"className":11905,"style":11906},[1928],"height:0.7719em;vertical-align:-0.136em;",[1854,11908,1908],{"className":11909},[1933,1934],[1854,11911],{"className":11912,"style":1940},[1939],[1854,11914,11857],{"className":11915},[1944],[1854,11917],{"className":11918,"style":1940},[1939],[1854,11920,11922,11926,12086,12089],{"className":11921},[1924],[1854,11923],{"className":11924,"style":11925},[1928],"height:2.0658em;vertical-align:-0.686em;",[1854,11927,11929,12061],{"className":11928},[2026],[1854,11930,11932,11939,12055],{"className":11931},[2026],[1854,11933,11935],{"className":11934,"style":3511},[1958,3510],[1854,11936,1883],{"className":11937},[3515,11938],"size2",[1854,11940,11942,11945,12052],{"className":11941},[1933],[1854,11943],{"className":11944},[1958,3163],[1854,11946,11948],{"className":11947},[3081],[1854,11949,11951,12044],{"className":11950},[1972,1973],[1854,11952,11954,12041],{"className":11953},[1977],[1854,11955,11958,11969,11977],{"className":11956,"style":11957},[1981],"height:1.1758em;",[1854,11959,11960,11963],{"style":5251},[1854,11961],{"className":11962,"style":2944},[1989],[1854,11964,11966],{"className":11965},[1933],[1854,11967,6989],{"className":11968,"style":3970},[1933,1934],[1854,11970,11971,11974],{"style":3254},[1854,11972],{"className":11973,"style":2944},[1989],[1854,11975],{"className":11976,"style":3262},[3261],[1854,11978,11980,11983],{"style":11979},"top:-3.7452em;",[1854,11981],{"className":11982,"style":2944},[1989],[1854,11984,11986,12038],{"className":11985},[1933],[1854,11987,11989,11992],{"className":11988},[1933],[1854,11990,3412],{"className":11991,"style":3562},[1933,1934],[1854,11993,11995],{"className":11994},[1968],[1854,11996,11998,12030],{"className":11997},[1972,1973],[1854,11999,12001,12027],{"className":12000},[1977],[1854,12002,12004],{"className":12003,"style":3575},[1981],[1854,12005,12006,12009],{"style":3578},[1854,12007],{"className":12008,"style":1990},[1989],[1854,12010,12012],{"className":12011},[1994,1995,1996,1997],[1854,12013,12015,12018,12021,12024],{"className":12014},[1933,1997],[1854,12016,1892],{"className":12017},[1933,1997],[1854,12019,2294],{"className":12020},[2415,1997],[1854,12022,2297],{"className":12023,"style":2429},[1933,1934,1997],[1854,12025,3600],{"className":12026},[1933,1997],[1854,12028,2005],{"className":12029},[2004],[1854,12031,12033],{"className":12032},[1977],[1854,12034,12036],{"className":12035,"style":3610},[1981],[1854,12037],{},[1854,12039,2857],{"className":12040,"style":3000},[1933,1934],[1854,12042,2005],{"className":12043},[2004],[1854,12045,12047],{"className":12046},[1977],[1854,12048,12050],{"className":12049,"style":5364},[1981],[1854,12051],{},[1854,12053],{"className":12054},[2080,3163],[1854,12056,12058],{"className":12057,"style":3511},[2080,3510],[1854,12059,1911],{"className":12060},[3515,11938],[1854,12062,12064],{"className":12063},[1968],[1854,12065,12067],{"className":12066},[1972],[1854,12068,12070],{"className":12069},[1977],[1854,12071,12074],{"className":12072,"style":12073},[1981],"height:1.3798em;",[1854,12075,12077,12080],{"style":12076},"top:-3.6287em;margin-right:0.05em;",[1854,12078],{"className":12079,"style":1990},[1989],[1854,12081,12083],{"className":12082},[1994,1995,1996,1997],[1854,12084,2860],{"className":12085},[1933,1997],[1854,12087],{"className":12088,"style":2022},[1939],[1854,12090,3125],{"className":12091},[1933],[1793,12093,12094,12095,12147],{},"比例估计在最保守的 ",[1854,12096,12098,12117],{"className":12097},[1857],[1854,12099,12101],{"className":12100},[1861],[1863,12102,12103],{"xmlns":1865},[1867,12104,12105,12114],{},[1870,12106,12107,12109,12111],{},[1873,12108,1793],{},[1877,12110,1879],{},[1890,12112,12113],{},"0.5",[1913,12115,12116],{"encoding":1915},"p=0.5",[1854,12118,12120,12138],{"className":12119,"ariaHidden":1895},[1920],[1854,12121,12123,12126,12129,12132,12135],{"className":12122},[1924],[1854,12124],{"className":12125,"style":2425},[1928],[1854,12127,1793],{"className":12128},[1933,1934],[1854,12130],{"className":12131,"style":1940},[1939],[1854,12133,1879],{"className":12134},[1944],[1854,12136],{"className":12137,"style":1940},[1939],[1854,12139,12141,12144],{"className":12140},[1924],[1854,12142],{"className":12143,"style":9561},[1928],[1854,12145,12113],{"className":12146},[1933]," 下：",[1854,12149,12151],{"className":12150},[2118],[1854,12152,12154,12202],{"className":12153},[1857],[1854,12155,12157],{"className":12156},[1861],[1863,12158,12159],{"xmlns":1865,"display":2127},[1867,12160,12161,12199],{},[1870,12162,12163,12165,12167,12197],{},[1873,12164,1908],{},[1877,12166,11857],{},[3081,12168,12169,12187],{},[5200,12170,12171,12173,12185],{},[1873,12172,3412],{},[1870,12174,12175,12177,12179,12181,12183],{},[1890,12176,1892],{},[1877,12178,2294],{},[1873,12180,2297],{},[1873,12182,3102],{"mathvariant":2525},[1890,12184,2860],{},[1890,12186,2860],{},[1870,12188,12189,12191],{},[1890,12190,9019],{},[2853,12192,12193,12195],{},[1873,12194,6989],{},[1890,12196,2860],{},[1873,12198,3125],{"mathvariant":2525},[1913,12200,12201],{"encoding":1915},"n\\ge\n\\frac{z_{1-\\alpha\u002F2}^2}{4E^2}.",[1854,12203,12205,12223],{"className":12204,"ariaHidden":1895},[1920],[1854,12206,12208,12211,12214,12217,12220],{"className":12207},[1924],[1854,12209],{"className":12210,"style":11906},[1928],[1854,12212,1908],{"className":12213},[1933,1934],[1854,12215],{"className":12216,"style":1940},[1939],[1854,12218,11857],{"className":12219},[1944],[1854,12221],{"className":12222,"style":1940},[1939],[1854,12224,12226,12230,12385],{"className":12225},[1924],[1854,12227],{"className":12228,"style":12229},[1928],"height:2.3871em;vertical-align:-0.686em;",[1854,12231,12233,12236,12382],{"className":12232},[1933],[1854,12234],{"className":12235},[1958,3163],[1854,12237,12239],{"className":12238},[3081],[1854,12240,12242,12374],{"className":12241},[1972,1973],[1854,12243,12245,12371],{"className":12244},[1977],[1854,12246,12249,12289,12297],{"className":12247,"style":12248},[1981],"height:1.7011em;",[1854,12250,12251,12254],{"style":5251},[1854,12252],{"className":12253,"style":2944},[1989],[1854,12255,12257,12260],{"className":12256},[1933],[1854,12258,9019],{"className":12259},[1933],[1854,12261,12263,12266],{"className":12262},[1933],[1854,12264,6989],{"className":12265,"style":3970},[1933,1934],[1854,12267,12269],{"className":12268},[1968],[1854,12270,12272],{"className":12271},[1972],[1854,12273,12275],{"className":12274},[1977],[1854,12276,12278],{"className":12277,"style":5276},[1981],[1854,12279,12280,12283],{"style":5279},[1854,12281],{"className":12282,"style":1990},[1989],[1854,12284,12286],{"className":12285},[1994,1995,1996,1997],[1854,12287,2860],{"className":12288},[1933,1997],[1854,12290,12291,12294],{"style":3254},[1854,12292],{"className":12293,"style":2944},[1989],[1854,12295],{"className":12296,"style":3262},[3261],[1854,12298,12300,12303],{"style":12299},"top:-3.887em;",[1854,12301],{"className":12302,"style":2944},[1989],[1854,12304,12306],{"className":12305},[1933],[1854,12307,12309,12312],{"className":12308},[1933],[1854,12310,3412],{"className":12311,"style":3562},[1933,1934],[1854,12313,12315],{"className":12314},[1968],[1854,12316,12318,12362],{"className":12317},[1972,1973],[1854,12319,12321,12359],{"className":12320},[1977],[1854,12322,12324,12348],{"className":12323,"style":3013},[1981],[1854,12325,12327,12330],{"style":12326},"top:-2.378em;margin-left:-0.044em;margin-right:0.05em;",[1854,12328],{"className":12329,"style":1990},[1989],[1854,12331,12333],{"className":12332},[1994,1995,1996,1997],[1854,12334,12336,12339,12342,12345],{"className":12335},[1933,1997],[1854,12337,1892],{"className":12338},[1933,1997],[1854,12340,2294],{"className":12341},[2415,1997],[1854,12343,2297],{"className":12344,"style":2429},[1933,1934,1997],[1854,12346,3600],{"className":12347},[1933,1997],[1854,12349,12350,12353],{"style":3016},[1854,12351],{"className":12352,"style":1990},[1989],[1854,12354,12356],{"className":12355},[1994,1995,1996,1997],[1854,12357,2860],{"className":12358},[1933,1997],[1854,12360,2005],{"className":12361},[2004],[1854,12363,12365],{"className":12364},[1977],[1854,12366,12369],{"className":12367,"style":12368},[1981],"height:0.497em;",[1854,12370],{},[1854,12372,2005],{"className":12373},[2004],[1854,12375,12377],{"className":12376},[1977],[1854,12378,12380],{"className":12379,"style":5364},[1981],[1854,12381],{},[1854,12383],{"className":12384},[2080,3163],[1854,12386,3125],{"className":12387},[1933],[1793,12389,12390],{},"真实研究还要考虑失访、设计效应、聚类、有限总体修正和多重结果。",[1816,12392,12394],{"id":12393},"_10-与贝叶斯可信区间的区别","10. 与贝叶斯可信区间的区别",[1793,12396,12397],{},"贝叶斯可信区间基于后验分布：",[1854,12399,12401],{"className":12400},[2118],[1854,12402,12404,12443],{"className":12403},[1857],[1854,12405,12407],{"className":12406},[1861],[1863,12408,12409],{"xmlns":1865,"display":2127},[1867,12410,12411,12440],{},[1870,12412,12413,12415,12417,12419,12421,12423,12426,12428,12430,12432,12434,12436,12438],{},[1873,12414,2266],{},[1877,12416,1883],{"stretchy":1882},[1873,12418,2096],{},[1877,12420,2276],{},[1873,12422,2134],{},[1877,12424,12425],{},"∣",[1873,12427,1875],{},[1877,12429,1911],{"stretchy":1882},[1877,12431,1879],{},[1890,12433,1892],{},[1877,12435,2294],{},[1873,12437,2297],{},[1873,12439,3125],{"mathvariant":2525},[1913,12441,12442],{"encoding":1915},"P(\\theta\\in C\\mid X)=1-\\alpha.",[1854,12444,12446,12470,12488,12509,12527],{"className":12445,"ariaHidden":1895},[1920],[1854,12447,12449,12452,12455,12458,12461,12464,12467],{"className":12448},[1924],[1854,12450],{"className":12451,"style":1954},[1928],[1854,12453,2266],{"className":12454,"style":2318},[1933,1934],[1854,12456,1883],{"className":12457},[1958],[1854,12459,2096],{"className":12460,"style":2113},[1933,1934],[1854,12462],{"className":12463,"style":1940},[1939],[1854,12465,2276],{"className":12466},[1944],[1854,12468],{"className":12469,"style":1940},[1939],[1854,12471,12473,12476,12479,12482,12485],{"className":12472},[1924],[1854,12474],{"className":12475,"style":1954},[1928],[1854,12477,2134],{"className":12478,"style":2184},[1933,1934],[1854,12480],{"className":12481,"style":1940},[1939],[1854,12483,12425],{"className":12484},[1944],[1854,12486],{"className":12487,"style":1940},[1939],[1854,12489,12491,12494,12497,12500,12503,12506],{"className":12490},[1924],[1854,12492],{"className":12493,"style":1954},[1928],[1854,12495,1875],{"className":12496,"style":1935},[1933,1934],[1854,12498,1911],{"className":12499},[2080],[1854,12501],{"className":12502,"style":1940},[1939],[1854,12504,1879],{"className":12505},[1944],[1854,12507],{"className":12508,"style":1940},[1939],[1854,12510,12512,12515,12518,12521,12524],{"className":12511},[1924],[1854,12513],{"className":12514,"style":2404},[1928],[1854,12516,1892],{"className":12517},[1933],[1854,12519],{"className":12520,"style":2411},[1939],[1854,12522,2294],{"className":12523},[2415],[1854,12525],{"className":12526,"style":2411},[1939],[1854,12528,12530,12533,12536],{"className":12529},[1924],[1854,12531],{"className":12532,"style":2484},[1928],[1854,12534,2297],{"className":12535,"style":2429},[1933,1934],[1854,12537,3125],{"className":12538},[1933],[1793,12540,12541],{},"这里参数在后验中是随机量，因此可以给出条件于数据和先验的概率陈述。频率置信区间评价重复抽样覆盖；贝叶斯可信区间评价后验概率。两者在大样本和弱先验下可能接近，但概念与保证不同。",[1816,12543,12544],{"id":12544},"常见错误",[1797,12546,12547,12550,12553,12556,12559,12562,12565],{},[1800,12548,12549],{},"把 95% 置信区间解释成“真参数有 95% 概率在里面”；",[1800,12551,12552],{},"只报告区间是否包含 0，不解释单位和经济或科学意义；",[1800,12554,12555],{},"对小样本比例机械使用 Wald 区间；",[1800,12557,12558],{},"忽略配对、聚类、时间相关或复杂抽样设计；",[1800,12560,12561],{},"把非显著结果解释为“证明没有效应”；",[1800,12563,12564],{},"只追求窄区间，却不检查覆盖率和模型设定；",[1800,12566,12567],{},"Bootstrap 时按观测重抽样，却破坏了原数据的依赖结构。",[1816,12569,12570],{"id":12570},"自测题",[1797,12572,12573,12576,12579,12582,12585],{},[1800,12574,12575],{},"为什么观测到一个 95% 置信区间后，频率学派不说参数有 95% 概率在其中？",[1800,12577,12578],{},"正态均值在方差未知时为什么使用 t 而不是 z？",[1800,12580,12581],{},"稀有事件比例为什么常优先使用 Wilson 而不是 Wald？",[1800,12583,12584],{},"区间不包含 0 是否足以说明结果重要？",[1800,12586,12587],{},"时间序列均值做 Bootstrap 时，为什么不能随意逐点重抽样？",[1816,12589,12590],{"id":12590},"答案指引",[1797,12592,12593,12596,12743,12746,12749],{},[1800,12594,12595],{},"参数被视为固定，随机的是由样本决定的区间；95% 是构造程序的长期覆盖率。",[1800,12597,12598,12599,12627,12628,12656,12657,12742],{},"用 ",[1854,12600,12602,12615],{"className":12601},[1857],[1854,12603,12605],{"className":12604},[1861],[1863,12606,12607],{"xmlns":1865},[1867,12608,12609,12613],{},[1870,12610,12611],{},[1873,12612,3955],{},[1913,12614,3955],{"encoding":1915},[1854,12616,12618],{"className":12617,"ariaHidden":1895},[1920],[1854,12619,12621,12624],{"className":12620},[1924],[1854,12622],{"className":12623,"style":1929},[1928],[1854,12625,3955],{"className":12626,"style":3970},[1933,1934]," 估计 ",[1854,12629,12631,12644],{"className":12630},[1857],[1854,12632,12634],{"className":12633},[1861],[1863,12635,12636],{"xmlns":1865},[1867,12637,12638,12642],{},[1870,12639,12640],{},[1873,12641,2857],{},[1913,12643,3046],{"encoding":1915},[1854,12645,12647],{"className":12646,"ariaHidden":1895},[1920],[1854,12648,12650,12653],{"className":12649},[1924],[1854,12651],{"className":12652,"style":2484},[1928],[1854,12654,2857],{"className":12655,"style":3000},[1933,1934]," 带来额外随机性，标准化统计量服从 ",[1854,12658,12660,12684],{"className":12659},[1857],[1854,12661,12663],{"className":12662},[1861],[1863,12664,12665],{"xmlns":1865},[1867,12666,12667,12681],{},[1870,12668,12669],{},[1885,12670,12671,12673],{},[1873,12672,4051],{},[1870,12674,12675,12677,12679],{},[1873,12676,1908],{},[1877,12678,2294],{},[1890,12680,1892],{},[1913,12682,12683],{"encoding":1915},"t_{n-1}",[1854,12685,12687],{"className":12686,"ariaHidden":1895},[1920],[1854,12688,12690,12693],{"className":12689},[1924],[1854,12691],{"className":12692,"style":4256},[1928],[1854,12694,12696,12699],{"className":12695},[1933],[1854,12697,4051],{"className":12698},[1933,1934],[1854,12700,12702],{"className":12701},[1968],[1854,12703,12705,12734],{"className":12704},[1972,1973],[1854,12706,12708,12731],{"className":12707},[1977],[1854,12709,12711],{"className":12710,"style":1982},[1981],[1854,12712,12713,12716],{"style":4277},[1854,12714],{"className":12715,"style":1990},[1989],[1854,12717,12719],{"className":12718},[1994,1995,1996,1997],[1854,12720,12722,12725,12728],{"className":12721},[1933,1997],[1854,12723,1908],{"className":12724},[1933,1934,1997],[1854,12726,2294],{"className":12727},[2415,1997],[1854,12729,1892],{"className":12730},[1933,1997],[1854,12732,2005],{"className":12733},[2004],[1854,12735,12737],{"className":12736},[1977],[1854,12738,12740],{"className":12739,"style":4305},[1981],[1854,12741],{},"。",[1800,12744,12745],{},"Wald 正态近似在参数边界和小样本下失真，Wilson 由 score 反演而来，覆盖通常更稳定。",[1800,12747,12748],{},"不足。还要解释效应大小、单位、区间宽度、研究设计、成本和实际意义。",[1800,12750,12751],{},"逐点重抽样破坏自相关结构，使 Bootstrap 分布不能模拟真实抽样机制；应考虑 block bootstrap 等方法。",[1816,12753,12754],{"id":12754},"进一步阅读",[1823,12756,12757,12765,12772,12775,12782],{},[1800,12758,12759,12760,12764],{},"Casella and Berger, ",[12761,12762,12763],"em",{},"Statistical Inference","：枢轴量与区间估计理论；",[1800,12766,12767,12768,12771],{},"Wasserman, ",[12761,12769,12770],{},"All of Statistics","：渐近区间与现代统计概览；",[1800,12773,12774],{},"Brown, Cai and DasGupta (2001)：二项比例区间的系统比较；",[1800,12776,12777,12778,12781],{},"Efron and Tibshirani, ",[12761,12779,12780],{},"An Introduction to the Bootstrap","；",[1800,12783,12784,12785,12742],{},"Davison and Hinkley, ",[12761,12786,12787],{},"Bootstrap Methods and Their Application",[1793,12789,12790,12794,12795],{},[2613,12791,12793],{"href":12792},"..\u002F01-sampling\u002F","上一章：抽样分布"," · ",[2613,12796,12798],{"href":12797},"..\u002F03-point-estimation\u002F","下一章：点估计理论",{"title":10,"searchDepth":12800,"depth":12800,"links":12801},2,[12802,12803,12804,12810,12811,12816,12819,12820,12821,12824,12825,12826,12827,12828,12829],{"id":1818,"depth":12800,"text":1818},{"id":1848,"depth":12800,"text":1849},{"id":2583,"depth":12800,"text":2584,"children":12805},[12806,12808,12809],{"id":2799,"depth":12807,"text":2800},3,{"id":3936,"depth":12807,"text":3937},{"id":4930,"depth":12807,"text":4931},{"id":4949,"depth":12800,"text":4950},{"id":6089,"depth":12800,"text":6090,"children":12812},[12813,12814,12815],{"id":6093,"depth":12807,"text":6094},{"id":6769,"depth":12807,"text":6770},{"id":7023,"depth":12807,"text":7024},{"id":8041,"depth":12800,"text":8042,"children":12817},[12818],{"id":9508,"depth":12807,"text":9508},{"id":9691,"depth":12800,"text":9692},{"id":10902,"depth":12800,"text":10903},{"id":11196,"depth":12800,"text":11197,"children":12822},[12823],{"id":11762,"depth":12807,"text":11763},{"id":11781,"depth":12800,"text":11782},{"id":12393,"depth":12800,"text":12394},{"id":12544,"depth":12800,"text":12544},{"id":12570,"depth":12800,"text":12570},{"id":12590,"depth":12800,"text":12590},{"id":12754,"depth":12800,"text":12754},"从枢轴量、t 区间和 Wilson 区间进入渐近、似然与 Bootstrap 置信区间，并检查重复抽样覆盖率。","md",{"sidebar":12833},{"order":12834},8,true,{"title":1692,"description":12830},"ZfdElgXVkb6HbiCnZaUPiMr8nLdy8wqQDABbxywm5HU",[12839,12841],{"title":1686,"path":1687,"stem":1688,"description":12840,"children":-1},"把统计量视为随机变量，连接样本均值、样本方差、卡方、t、F 与次序统计量。",{"title":1698,"path":1699,"stem":1700,"description":12842,"children":-1},"用偏差、方差、MSE、一致性、充分性、效率与稳健性评价估计量。",1785754756990]