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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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是随机变量。",[1796,2127,2128],{},"偏差：",[1840,2130,2133],{"className":2131},[2132],"katex-display",[1840,2134,2136,2201],{"className":2135},[1843],[1840,2137,2139],{"className":2138},[1847],[1849,2140,2142],{"xmlns":1851,"display":2141},"block",[1853,2143,2144,2198],{},[1856,2145,2146,2159,2161,2167,2169,2171,2178,2181,2187,2190,2193,2195],{},[1881,2147,2148,2157],{},[1856,2149,2150,2154],{},[1863,2151,2153],{"mathvariant":2152},"normal","Bias",[1867,2155,2156],{},"⁡",[1863,2158,1865],{},[1867,2160,1879],{"stretchy":1878},[1859,2162,2163,2165],{"accent":1861},[1863,2164,1865],{},[1867,2166,1869],{"stretchy":1861},[1867,2168,1907],{"stretchy":1878},[1867,2170,1872],{},[1881,2172,2173,2176],{},[1863,2174,2175],{},"E",[1863,2177,1865],{},[1867,2179,2180],{"stretchy":1878},"[",[1859,2182,2183,2185],{"accent":1861},[1863,2184,1865],{},[1867,2186,1869],{"stretchy":1861},[1867,2188,2189],{"stretchy":1878},"]",[1867,2191,2192],{},"−",[1863,2194,1865],{},[1863,2196,2197],{"mathvariant":2152},".",[1909,2199,2200],{"encoding":1911},"\\operatorname{Bias}_\\theta(\\widehat\\theta)\n=E_\\theta[\\widehat\\theta]-\\theta.",[1840,2202,2204,2305,2402],{"className":2203,"ariaHidden":1861},[1916],[1840,2205,2207,2211,2258,2261,2293,2296,2299,2302],{"className":2206},[1920],[1840,2208],{"className":2209,"style":2210},[1924],"height:1.1844em;vertical-align:-0.25em;",[1840,2212,2215,2222],{"className":2213},[2214],"mop",[1840,2216,2218],{"className":2217},[2214],[1840,2219,2153],{"className":2220},[1929,2221],"mathrm",[1840,2223,2225],{"className":2224},[2016],[1840,2226,2228,2250],{"className":2227},[1934,2020],[1840,2229,2231,2247],{"className":2230},[1938],[1840,2232,2235],{"className":2233,"style":2234},[1942],"height:0.3361em;",[1840,2236,2238,2241],{"style":2237},"top:-2.55em;margin-right:0.05em;",[1840,2239],{"className":2240,"style":2034},[1949],[1840,2242,2244],{"className":2243},[2038,2039,2040,2041],[1840,2245,1865],{"className":2246,"style":1955},[1929,1954,2041],[1840,2248,2049],{"className":2249},[2048],[1840,2251,2253],{"className":2252},[1938],[1840,2254,2256],{"className":2255,"style":2056},[1942],[1840,2257],{},[1840,2259,1879],{"className":2260},[2005],[1840,2262,2264],{"className":2263},[1929,1930],[1840,2265,2267],{"className":2266},[1934],[1840,2268,2270],{"className":2269},[1938],[1840,2271,2273,2281],{"className":2272,"style":1925},[1942],[1840,2274,2275,2278],{"style":1945},[1840,2276],{"className":2277,"style":1950},[1949],[1840,2279,1865],{"className":2280,"style":1955},[1929,1954],[1840,2282,2284,2287],{"className":2283,"style":1960},[1959],[1840,2285],{"className":2286,"style":1950},[1949],[1840,2288,2289],{"style":1966},[1968,2290,2291],{"xmlns":1970,"width":1971,"height":1972,"viewBox":1973,"preserveAspectRatio":1974},[1976,2292],{"d":1978},[1840,2294,1907],{"className":2295},[2124],[1840,2297],{"className":2298,"style":1983},[1982],[1840,2300,1872],{"className":2301},[1987],[1840,2303],{"className":2304,"style":1983},[1982],[1840,2306,2308,2311,2353,2356,2388,2391,2395,2399],{"className":2307},[1920],[1840,2309],{"className":2310,"style":2210},[1924],[1840,2312,2314,2318],{"className":2313},[1929],[1840,2315,2175],{"className":2316,"style":2317},[1929,1954],"margin-right:0.0576em;",[1840,2319,2321],{"className":2320},[2016],[1840,2322,2324,2345],{"className":2323},[1934,2020],[1840,2325,2327,2342],{"className":2326},[1938],[1840,2328,2330],{"className":2329,"style":2234},[1942],[1840,2331,2333,2336],{"style":2332},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[1840,2334],{"className":2335,"style":2034},[1949],[1840,2337,2339],{"className":2338},[2038,2039,2040,2041],[1840,2340,1865],{"className":2341,"style":1955},[1929,1954,2041],[1840,2343,2049],{"className":2344},[2048],[1840,2346,2348],{"className":2347},[1938],[1840,2349,2351],{"className":2350,"style":2056},[1942],[1840,2352],{},[1840,2354,2180],{"className":2355},[2005],[1840,2357,2359],{"className":2358},[1929,1930],[1840,2360,2362],{"className":2361},[1934],[1840,2363,2365],{"className":2364},[1938],[1840,2366,2368,2376],{"className":2367,"style":1925},[1942],[1840,2369,2370,2373],{"style":1945},[1840,2371],{"className":2372,"style":1950},[1949],[1840,2374,1865],{"className":2375,"style":1955},[1929,1954],[1840,2377,2379,2382],{"className":2378,"style":1960},[1959],[1840,2380],{"className":2381,"style":1950},[1949],[1840,2383,2384],{"style":1966},[1968,2385,2386],{"xmlns":1970,"width":1971,"height":1972,"viewBox":1973,"preserveAspectRatio":1974},[1976,2387],{"d":1978},[1840,2389,2189],{"className":2390},[2124],[1840,2392],{"className":2393,"style":2394},[1982],"margin-right:0.2222em;",[1840,2396,2192],{"className":2397},[2398],"mbin",[1840,2400],{"className":2401,"style":2394},[1982],[1840,2403,2405,2409,2412],{"className":2404},[1920],[1840,2406],{"className":2407,"style":2408},[1924],"height:0.6944em;",[1840,2410,1865],{"className":2411,"style":1955},[1929,1954],[1840,2413,2197],{"className":2414},[1929],[1796,2416,2417],{},"均方误差：",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,[1959],[1840,2714],{"className":2715,"style":1950},[1949],[1840,2717,2718],{"style":1966},[1968,2719,2720],{"xmlns":1970,"width":1971,"height":1972,"viewBox":1973,"preserveAspectRatio":1974},[1976,2721],{"d":1978},[1840,2723],{"className":2724,"style":2394},[1982],[1840,2726,2192],{"className":2727},[2398],[1840,2729],{"className":2730,"style":2394},[1982],[1840,2732,2734,2738,2741,2772,2775,2778,2781],{"className":2733},[1920],[1840,2735],{"className":2736,"style":2737},[1924],"height:1.1141em;vertical-align:-0.25em;",[1840,2739,1865],{"className":2740,"style":1955},[1929,1954],[1840,2742,2744,2747],{"className":2743},[2124],[1840,2745,1907],{"className":2746},[2124],[1840,2748,2750],{"className":2749},[2016],[1840,2751,2753],{"className":2752},[1934],[1840,2754,2756],{"className":2755},[1938],[1840,2757,2760],{"className":2758,"style":2759},[1942],"height:0.8641em;",[1840,2761,2763,2766],{"style":2762},"top:-3.113em;margin-right:0.05em;",[1840,2764],{"className":2765,"style":2034},[1949],[1840,2767,2769],{"className":2768},[2038,2039,2040,2041],[1840,2770,2483],{"className":2771},[1929,2041],[1840,2773,2189],{"className":2774},[2124],[1840,2776],{"className":2777,"style":1983},[1982],[1840,2779,1872],{"className":2780},[1987],[1840,2782],{"className":2783,"style":1983},[1982],[1840,2785,2787,2790,2833,2836,2868,2871,2874,2877],{"className":2786},[1920],[1840,2788],{"className":2789,"style":2210},[1924],[1840,2791,2793,2799],{"className":2792},[2214],[1840,2794,2796],{"className":2795},[2214],[1840,2797,2494],{"className":2798},[1929,2221],[1840,2800,2802],{"className":2801},[2016],[1840,2803,2805,2825],{"className":2804},[1934,2020],[1840,2806,2808,2822],{"className":2807},[1938],[1840,2809,2811],{"className":2810,"style":2234},[1942],[1840,2812,2813,2816],{"style":2237},[1840,2814],{"className":2815,"style":2034},[1949],[1840,2817,2819],{"className":2818},[2038,2039,2040,2041],[1840,2820,1865],{"className":2821,"style":1955},[1929,1954,2041],[1840,2823,2049],{"className":2824},[2048],[1840,2826,2828],{"className":2827},[1938],[1840,2829,2831],{"className":2830,"style":2056},[1942],[1840,2832],{},[1840,2834,1879],{"className":2835},[2005],[1840,2837,2839],{"className":2838},[1929,1930],[1840,2840,2842],{"className":2841},[1934],[1840,2843,2845],{"className":2844},[1938],[1840,2846,2848,2856],{"className":2847,"style":1925},[1942],[1840,2849,2850,2853],{"style":1945},[1840,2851],{"className":2852,"style":1950},[1949],[1840,2854,1865],{"className":2855,"style":1955},[1929,1954],[1840,2857,2859,2862],{"className":2858,"style":1960},[1959],[1840,2860],{"className":2861,"style":1950},[1949],[1840,2863,2864],{"style":1966},[1968,2865,2866],{"xmlns":1970,"width":1971,"height":1972,"viewBox":1973,"preserveAspectRatio":1974},[1976,2867],{"d":1978},[1840,2869,1907],{"className":2870},[2124],[1840,2872],{"className":2873,"style":2394},[1982],[1840,2875,2511],{"className":2876},[2398],[1840,2878],{"className":2879,"style":2394},[1982],[1840,2881,2883,2886,2929,2932,2964,2993],{"className":2882},[1920],[1840,2884],{"className":2885,"style":2210},[1924],[1840,2887,2889,2895],{"className":2888},[2214],[1840,2890,2892],{"className":2891},[2214],[1840,2893,2153],{"className":2894},[1929,2221],[1840,2896,2898],{"className":2897},[2016],[1840,2899,2901,2921],{"className":2900},[1934,2020],[1840,2902,2904,2918],{"className":2903},[1938],[1840,2905,2907],{"className":2906,"style":2234},[1942],[1840,2908,2909,2912],{"style":2237},[1840,2910],{"className":2911,"style":2034},[1949],[1840,2913,2915],{"className":2914},[2038,2039,2040,2041],[1840,2916,1865],{"className":2917,"style":1955},[1929,1954,2041],[1840,2919,2049],{"className":2920},[2048],[1840,2922,2924],{"className":2923},[1938],[1840,2925,2927],{"className":2926,"style":2056},[1942],[1840,2928],{},[1840,2930,1879],{"className":2931},[2005],[1840,2933,2935],{"className":2934},[1929,1930],[1840,2936,2938],{"className":2937},[1934],[1840,2939,2941],{"className":2940},[1938],[1840,2942,2944,2952],{"className":2943,"style":1925},[1942],[1840,2945,2946,2949],{"style":1945},[1840,2947],{"className":2948,"style":1950},[1949],[1840,2950,1865],{"className":2951,"style":1955},[1929,1954],[1840,2953,2955,2958],{"className":2954,"style":1960},[1959],[1840,2956],{"className":2957,"style":1950},[1949],[1840,2959,2960],{"style":1966},[1968,2961,2962],{"xmlns":1970,"width":1971,"height":1972,"viewBox":1973,"preserveAspectRatio":1974},[1976,2963],{"d":1978},[1840,2965,2967,2970],{"className":2966},[2124],[1840,2968,1907],{"className":2969},[2124],[1840,2971,2973],{"className":2972},[2016],[1840,2974,2976],{"className":2975},[1934],[1840,2977,2979],{"className":2978},[1938],[1840,2980,2982],{"className":2981,"style":2759},[1942],[1840,2983,2984,2987],{"style":2762},[1840,2985],{"className":2986,"style":2034},[1949],[1840,2988,2990],{"className":2989},[2038,2039,2040,2041],[1840,2991,2483],{"className":2992},[1929,2041],[1840,2994,2197],{"className":2995},[1929],[1796,2997,2998],{},"无偏不保证 MSE 最小。轻微有偏但方差大幅降低的估计量可能更适合预测或决策。",[1807,3000,3002],{"id":3001},"_2-一致性与渐近正态","2. 一致性与渐近正态",[1796,3004,3005],{},"一致性：",[1840,3007,3009],{"className":3008},[2132],[1840,3010,3012,3051],{"className":3011},[1843],[1840,3013,3015],{"className":3014},[1847],[1849,3016,3017],{"xmlns":1851,"display":2141},[1853,3018,3019,3048],{},[1856,3020,3021,3031,3044,3046],{},[1881,3022,3023,3029],{},[1859,3024,3025,3027],{"accent":1861},[1863,3026,1865],{},[1867,3028,1869],{"stretchy":1861},[1863,3030,1904],{},[1859,3032,3033,3037],{},[1867,3034,3036],{"stretchy":1861,"minsize":3035},"3.0em","→",[3038,3039,3042],"mpadded",{"width":3040,"lspace":3041},"+0.6em","0.3em",[1863,3043,1796],{},[1863,3045,1865],{},[1863,3047,2197],{"mathvariant":2152},[1909,3049,3050],{"encoding":1911},"\\widehat\\theta_n\\xrightarrow{p}\\theta.",[1840,3052,3054,3200],{"className":3053,"ariaHidden":1861},[1916],[1840,3055,3057,3061,3131,3134,3197],{"className":3056},[1920],[1840,3058],{"className":3059,"style":3060},[1924],"height:1.0844em;vertical-align:-0.15em;",[1840,3062,3064,3096],{"className":3063},[1929],[1840,3065,3067],{"className":3066},[1929,1930],[1840,3068,3070],{"className":3069},[1934],[1840,3071,3073],{"className":3072},[1938],[1840,3074,3076,3084],{"className":3075,"style":1925},[1942],[1840,3077,3078,3081],{"style":1945},[1840,3079],{"className":3080,"style":1950},[1949],[1840,3082,1865],{"className":3083,"style":1955},[1929,1954],[1840,3085,3087,3090],{"className":3086,"style":1960},[1959],[1840,3088],{"className":3089,"style":1950},[1949],[1840,3091,3092],{"style":1966},[1968,3093,3094],{"xmlns":1970,"width":1971,"height":1972,"viewBox":1973,"preserveAspectRatio":1974},[1976,3095],{"d":1978},[1840,3097,3099],{"className":3098},[2016],[1840,3100,3102,3123],{"className":3101},[1934,2020],[1840,3103,3105,3120],{"className":3104},[1938],[1840,3106,3108],{"className":3107,"style":2098},[1942],[1840,3109,3111,3114],{"style":3110},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1840,3112],{"className":3113,"style":2034},[1949],[1840,3115,3117],{"className":3116},[2038,2039,2040,2041],[1840,3118,1904],{"className":3119},[1929,1954,2041],[1840,3121,2049],{"className":3122},[2048],[1840,3124,3126],{"className":3125},[1938],[1840,3127,3129],{"className":3128,"style":2056},[1942],[1840,3130],{},[1840,3132],{"className":3133,"style":1983},[1982],[1840,3135,3138],{"className":3136},[1987,3137],"x-arrow",[1840,3139,3141,3188],{"className":3140},[1934,2020],[1840,3142,3144,3185],{"className":3143},[1938],[1840,3145,3148,3164],{"className":3146,"style":3147},[1942],"height:0.9234em;",[1840,3149,3151,3154],{"style":3150},"top:-3.322em;",[1840,3152],{"className":3153,"style":2034},[1949],[1840,3155,3158],{"className":3156},[2038,2039,2040,2041,3157],"x-arrow-pad",[1840,3159,3161],{"className":3160},[1929,2041],[1840,3162,1796],{"className":3163},[1929,1954,2041],[1840,3165,3168,3171],{"className":3166,"style":3167},[1959],"top:-2.689em;",[1840,3169],{"className":3170,"style":2034},[1949],[1840,3172,3176],{"className":3173,"style":3175},[3174],"hide-tail","height:0.522em;min-width:1.469em;",[1968,3177,3182],{"xmlns":1970,"width":3178,"height":3179,"viewBox":3180,"preserveAspectRatio":3181},"400em","0.522em","0 0 400000 522","xMaxYMin slice",[1976,3183],{"d":3184},"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",[1840,3186,2049],{"className":3187},[2048],[1840,3189,3191],{"className":3190},[1938],[1840,3192,3195],{"className":3193,"style":3194},[1942],"height:0.011em;",[1840,3196],{},[1840,3198],{"className":3199,"style":1983},[1982],[1840,3201,3203,3206,3209],{"className":3202},[1920],[1840,3204],{"className":3205,"style":2408},[1924],[1840,3207,1865],{"className":3208,"style":1955},[1929,1954],[1840,3210,2197],{"className":3211},[1929],[1796,3213,3214,3215,3268],{},"它只描述 ",[1840,3216,3218,3237],{"className":3217},[1843],[1840,3219,3221],{"className":3220},[1847],[1849,3222,3223],{"xmlns":1851},[1853,3224,3225,3234],{},[1856,3226,3227,3229,3231],{},[1863,3228,1904],{},[1867,3230,3036],{},[1863,3232,3233],{"mathvariant":2152},"∞",[1909,3235,3236],{"encoding":1911},"n\\to\\infty",[1840,3238,3240,3259],{"className":3239,"ariaHidden":1861},[1916],[1840,3241,3243,3247,3250,3253,3256],{"className":3242},[1920],[1840,3244],{"className":3245,"style":3246},[1924],"height:0.4306em;",[1840,3248,1904],{"className":3249},[1929,1954],[1840,3251],{"className":3252,"style":1983},[1982],[1840,3254,3036],{"className":3255},[1987],[1840,3257],{"className":3258,"style":1983},[1982],[1840,3260,3262,3265],{"className":3261},[1920],[1840,3263],{"className":3264,"style":3246},[1924],[1840,3266,3233],{"className":3267},[1929],"，不说明当前样本误差小。常见的渐近正态形式：",[1840,3270,3272],{"className":3271},[2132],[1840,3273,3275,3340],{"className":3274},[1843],[1840,3276,3278],{"className":3277},[1847],[1849,3279,3280],{"xmlns":1851,"display":2141},[1853,3281,3282,3337],{},[1856,3283,3284,3289,3291,3301,3303,3305,3307,3316,3319,3321,3324,3326,3333,3335],{},[3285,3286,3287],"msqrt",{},[1863,3288,1904],{},[1867,3290,1879],{"stretchy":1878},[1881,3292,3293,3299],{},[1859,3294,3295,3297],{"accent":1861},[1863,3296,1865],{},[1867,3298,1869],{"stretchy":1861},[1863,3300,1904],{},[1867,3302,2192],{},[1863,3304,1865],{},[1867,3306,1907],{"stretchy":1878},[1859,3308,3309,3311],{},[1867,3310,3036],{"stretchy":1861,"minsize":3035},[3038,3312,3313],{"width":3040,"lspace":3041},[1863,3314,3315],{},"d",[1863,3317,3318],{},"N",[1867,3320,1879],{"stretchy":1878},[1887,3322,3323],{},"0",[1867,3325,1892],{"separator":1861},[1881,3327,3328,3331],{},[1863,3329,3330],{},"V",[1863,3332,1865],{},[1867,3334,1907],{"stretchy":1878},[1863,3336,2197],{"mathvariant":2152},[1909,3338,3339],{"encoding":1911},"\\sqrt n(\\widehat\\theta_n-\\theta)\n\\xrightarrow{d}N(0,V_\\theta).",[1840,3341,3343,3484,3554],{"className":3342,"ariaHidden":1861},[1916],[1840,3344,3346,3349,3403,3406,3475,3478,3481],{"className":3345},[1920],[1840,3347],{"className":3348,"style":2210},[1924],[1840,3350,3353],{"className":3351},[1929,3352],"sqrt",[1840,3354,3356,3394],{"className":3355},[1934,2020],[1840,3357,3359,3391],{"className":3358},[1938],[1840,3360,3363,3373],{"className":3361,"style":3362},[1942],"height:0.8492em;",[1840,3364,3366,3369],{"className":3365,"style":1945},[1959],[1840,3367],{"className":3368,"style":1950},[1949],[1840,3370,1904],{"className":3371,"style":3372},[1929,1954],"padding-left:0.833em;",[1840,3374,3376,3379],{"style":3375},"top:-2.8092em;",[1840,3377],{"className":3378,"style":1950},[1949],[1840,3380,3383],{"className":3381,"style":3382},[3174],"min-width:0.853em;height:1.08em;",[1968,3384,3388],{"xmlns":1970,"width":3178,"height":3385,"viewBox":3386,"preserveAspectRatio":3387},"1.08em","0 0 400000 1080","xMinYMin slice",[1976,3389],{"d":3390},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[1840,3392,2049],{"className":3393},[2048],[1840,3395,3397],{"className":3396},[1938],[1840,3398,3401],{"className":3399,"style":3400},[1942],"height:0.1908em;",[1840,3402],{},[1840,3404,1879],{"className":3405},[2005],[1840,3407,3409,3441],{"className":3408},[1929],[1840,3410,3412],{"className":3411},[1929,1930],[1840,3413,3415],{"className":3414},[1934],[1840,3416,3418],{"className":3417},[1938],[1840,3419,3421,3429],{"className":3420,"style":1925},[1942],[1840,3422,3423,3426],{"style":1945},[1840,3424],{"className":3425,"style":1950},[1949],[1840,3427,1865],{"className":3428,"style":1955},[1929,1954],[1840,3430,3432,3435],{"className":3431,"style":1960},[1959],[1840,3433],{"className":3434,"style":1950},[1949],[1840,3436,3437],{"style":1966},[1968,3438,3439],{"xmlns":1970,"width":1971,"height":1972,"viewBox":1973,"preserveAspectRatio":1974},[1976,3440],{"d":1978},[1840,3442,3444],{"className":3443},[2016],[1840,3445,3447,3467],{"className":3446},[1934,2020],[1840,3448,3450,3464],{"className":3449},[1938],[1840,3451,3453],{"className":3452,"style":2098},[1942],[1840,3454,3455,3458],{"style":3110},[1840,3456],{"className":3457,"style":2034},[1949],[1840,3459,3461],{"className":3460},[2038,2039,2040,2041],[1840,3462,1904],{"className":3463},[1929,1954,2041],[1840,3465,2049],{"className":3466},[2048],[1840,3468,3470],{"className":3469},[1938],[1840,3471,3473],{"className":3472,"style":2056},[1942],[1840,3474],{},[1840,3476],{"className":3477,"style":2394},[1982],[1840,3479,2192],{"className":3480},[2398],[1840,3482],{"className":3483,"style":2394},[1982],[1840,3485,3487,3491,3494,3497,3500,3551],{"className":3486},[1920],[1840,3488],{"className":3489,"style":3490},[1924],"height:1.3581em;vertical-align:-0.25em;",[1840,3492,1865],{"className":3493,"style":1955},[1929,1954],[1840,3495,1907],{"className":3496},[2124],[1840,3498],{"className":3499,"style":1983},[1982],[1840,3501,3503],{"className":3502},[1987,3137],[1840,3504,3506,3543],{"className":3505},[1934,2020],[1840,3507,3509,3540],{"className":3508},[1938],[1840,3510,3513,3527],{"className":3511,"style":3512},[1942],"height:1.1081em;",[1840,3514,3515,3518],{"style":3150},[1840,3516],{"className":3517,"style":2034},[1949],[1840,3519,3521],{"className":3520},[2038,2039,2040,2041,3157],[1840,3522,3524],{"className":3523},[1929,2041],[1840,3525,3315],{"className":3526},[1929,1954,2041],[1840,3528,3530,3533],{"className":3529,"style":3167},[1959],[1840,3531],{"className":3532,"style":2034},[1949],[1840,3534,3536],{"className":3535,"style":3175},[3174],[1968,3537,3538],{"xmlns":1970,"width":3178,"height":3179,"viewBox":3180,"preserveAspectRatio":3181},[1976,3539],{"d":3184},[1840,3541,2049],{"className":3542},[2048],[1840,3544,3546],{"className":3545},[1938],[1840,3547,3549],{"className":3548,"style":3194},[1942],[1840,3550],{},[1840,3552],{"className":3553,"style":1983},[1982],[1840,3555,3557,3560,3564,3567,3570,3573,3576,3617,3620],{"className":3556},[1920],[1840,3558],{"className":3559,"style":1997},[1924],[1840,3561,3318],{"className":3562,"style":3563},[1929,1954],"margin-right:0.109em;",[1840,3565,1879],{"className":3566},[2005],[1840,3568,3323],{"className":3569},[1929],[1840,3571,1892],{"className":3572},[2062],[1840,3574],{"className":3575,"style":2066},[1982],[1840,3577,3579,3582],{"className":3578},[1929],[1840,3580,3330],{"className":3581,"style":2394},[1929,1954],[1840,3583,3585],{"className":3584},[2016],[1840,3586,3588,3609],{"className":3587},[1934,2020],[1840,3589,3591,3606],{"className":3590},[1938],[1840,3592,3594],{"className":3593,"style":2234},[1942],[1840,3595,3597,3600],{"style":3596},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[1840,3598],{"className":3599,"style":2034},[1949],[1840,3601,3603],{"className":3602},[2038,2039,2040,2041],[1840,3604,1865],{"className":3605,"style":1955},[1929,1954,2041],[1840,3607,2049],{"className":3608},[2048],[1840,3610,3612],{"className":3611},[1938],[1840,3613,3615],{"className":3614,"style":2056},[1942],[1840,3616],{},[1840,3618,1907],{"className":3619},[2124],[1840,3621,2197],{"className":3622},[1929],[1796,3624,3625],{},"这给出标准误与区间近似，但仍需检查有限样本偏差、边界、弱识别和维度增长。",[1807,3627,3629],{"id":3628},"_3-充分性压缩而不丢参数信息","3. 充分性：压缩而不丢参数信息",[1796,3631,3632,3633,3677,3678,3707,3708,3737,3738,3766],{},"统计量 ",[1840,3634,3636,3656],{"className":3635},[1843],[1840,3637,3639],{"className":3638},[1847],[1849,3640,3641],{"xmlns":1851},[1853,3642,3643,3653],{},[1856,3644,3645,3647,3649,3651],{},[1863,3646,1875],{},[1867,3648,1879],{"stretchy":1878},[1863,3650,1885],{},[1867,3652,1907],{"stretchy":1878},[1909,3654,3655],{"encoding":1911},"T(X)",[1840,3657,3659],{"className":3658,"ariaHidden":1861},[1916],[1840,3660,3662,3665,3668,3671,3674],{"className":3661},[1920],[1840,3663],{"className":3664,"style":1997},[1924],[1840,3666,1875],{"className":3667,"style":2001},[1929,1954],[1840,3669,1879],{"className":3670},[2005],[1840,3672,1885],{"className":3673,"style":2012},[1929,1954],[1840,3675,1907],{"className":3676},[2124]," 对 ",[1840,3679,3681,3695],{"className":3680},[1843],[1840,3682,3684],{"className":3683},[1847],[1849,3685,3686],{"xmlns":1851},[1853,3687,3688,3692],{},[1856,3689,3690],{},[1863,3691,1865],{},[1909,3693,3694],{"encoding":1911},"\\theta",[1840,3696,3698],{"className":3697,"ariaHidden":1861},[1916],[1840,3699,3701,3704],{"className":3700},[1920],[1840,3702],{"className":3703,"style":2408},[1924],[1840,3705,1865],{"className":3706,"style":1955},[1929,1954]," 充分，如果给定 ",[1840,3709,3711,3724],{"className":3710},[1843],[1840,3712,3714],{"className":3713},[1847],[1849,3715,3716],{"xmlns":1851},[1853,3717,3718,3722],{},[1856,3719,3720],{},[1863,3721,1875],{},[1909,3723,1875],{"encoding":1911},[1840,3725,3727],{"className":3726,"ariaHidden":1861},[1916],[1840,3728,3730,3734],{"className":3729},[1920],[1840,3731],{"className":3732,"style":3733},[1924],"height:0.6833em;",[1840,3735,1875],{"className":3736,"style":2001},[1929,1954]," 后样本的条件分布不再依赖 ",[1840,3739,3741,3754],{"className":3740},[1843],[1840,3742,3744],{"className":3743},[1847],[1849,3745,3746],{"xmlns":1851},[1853,3747,3748,3752],{},[1856,3749,3750],{},[1863,3751,1865],{},[1909,3753,3694],{"encoding":1911},[1840,3755,3757],{"className":3756,"ariaHidden":1861},[1916],[1840,3758,3760,3763],{"className":3759},[1920],[1840,3761],{"className":3762,"style":2408},[1924],[1840,3764,1865],{"className":3765,"style":1955},[1929,1954],"。",[1796,3768,3769],{},"因子分解定理：",[1840,3771,3773],{"className":3772},[2132],[1840,3774,3776,3834],{"className":3775},[1843],[1840,3777,3779],{"className":3778},[1847],[1849,3780,3781],{"xmlns":1851,"display":2141},[1853,3782,3783,3831],{},[1856,3784,3785,3792,3794,3797,3799,3801,3808,3810,3812,3814,3816,3818,3820,3823,3825,3827,3829],{},[1881,3786,3787,3790],{},[1863,3788,3789],{},"f",[1863,3791,1865],{},[1867,3793,1879],{"stretchy":1878},[1863,3795,3796],{},"x",[1867,3798,1907],{"stretchy":1878},[1867,3800,1872],{},[1881,3802,3803,3806],{},[1863,3804,3805],{},"g",[1863,3807,1865],{},[1867,3809,1879],{"stretchy":1878},[1863,3811,1875],{},[1867,3813,1879],{"stretchy":1878},[1863,3815,3796],{},[1867,3817,1907],{"stretchy":1878},[1867,3819,1907],{"stretchy":1878},[1863,3821,3822],{},"h",[1867,3824,1879],{"stretchy":1878},[1863,3826,3796],{},[1867,3828,1907],{"stretchy":1878},[1863,3830,2197],{"mathvariant":2152},[1909,3832,3833],{"encoding":1911},"f_\\theta(x)=g_\\theta(T(x))h(x).",[1840,3835,3837,3903],{"className":3836,"ariaHidden":1861},[1916],[1840,3838,3840,3843,3885,3888,3891,3894,3897,3900],{"className":3839},[1920],[1840,3841],{"className":3842,"style":1997},[1924],[1840,3844,3846,3850],{"className":3845},[1929],[1840,3847,3789],{"className":3848,"style":3849},[1929,1954],"margin-right:0.1076em;",[1840,3851,3853],{"className":3852},[2016],[1840,3854,3856,3877],{"className":3855},[1934,2020],[1840,3857,3859,3874],{"className":3858},[1938],[1840,3860,3862],{"className":3861,"style":2234},[1942],[1840,3863,3865,3868],{"style":3864},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[1840,3866],{"className":3867,"style":2034},[1949],[1840,3869,3871],{"className":3870},[2038,2039,2040,2041],[1840,3872,1865],{"className":3873,"style":1955},[1929,1954,2041],[1840,3875,2049],{"className":3876},[2048],[1840,3878,3880],{"className":3879},[1938],[1840,3881,3883],{"className":3882,"style":2056},[1942],[1840,3884],{},[1840,3886,1879],{"className":3887},[2005],[1840,3889,3796],{"className":3890},[1929,1954],[1840,3892,1907],{"className":3893},[2124],[1840,3895],{"className":3896,"style":1983},[1982],[1840,3898,1872],{"className":3899},[1987],[1840,3901],{"className":3902,"style":1983},[1982],[1840,3904,3906,3909,3951,3954,3957,3960,3963,3967,3970,3973,3976,3979],{"className":3905},[1920],[1840,3907],{"className":3908,"style":1997},[1924],[1840,3910,3912,3916],{"className":3911},[1929],[1840,3913,3805],{"className":3914,"style":3915},[1929,1954],"margin-right:0.0359em;",[1840,3917,3919],{"className":3918},[2016],[1840,3920,3922,3943],{"className":3921},[1934,2020],[1840,3923,3925,3940],{"className":3924},[1938],[1840,3926,3928],{"className":3927,"style":2234},[1942],[1840,3929,3931,3934],{"style":3930},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1840,3932],{"className":3933,"style":2034},[1949],[1840,3935,3937],{"className":3936},[2038,2039,2040,2041],[1840,3938,1865],{"className":3939,"style":1955},[1929,1954,2041],[1840,3941,2049],{"className":3942},[2048],[1840,3944,3946],{"className":3945},[1938],[1840,3947,3949],{"className":3948,"style":2056},[1942],[1840,3950],{},[1840,3952,1879],{"className":3953},[2005],[1840,3955,1875],{"className":3956,"style":2001},[1929,1954],[1840,3958,1879],{"className":3959},[2005],[1840,3961,3796],{"className":3962},[1929,1954],[1840,3964,3966],{"className":3965},[2124],"))",[1840,3968,3822],{"className":3969},[1929,1954],[1840,3971,1879],{"className":3972},[2005],[1840,3974,3796],{"className":3975},[1929,1954],[1840,3977,1907],{"className":3978},[2124],[1840,3980,2197],{"className":3981},[1929],[1796,3983,3984,3985,4013,4014,4043],{},"若 ",[1840,3986,3988,4001],{"className":3987},[1843],[1840,3989,3991],{"className":3990},[1847],[1849,3992,3993],{"xmlns":1851},[1853,3994,3995,3999],{},[1856,3996,3997],{},[1863,3998,1875],{},[1909,4000,1875],{"encoding":1911},[1840,4002,4004],{"className":4003,"ariaHidden":1861},[1916],[1840,4005,4007,4010],{"className":4006},[1920],[1840,4008],{"className":4009,"style":3733},[1924],[1840,4011,1875],{"className":4012,"style":2001},[1929,1954]," 充分，Rao–Blackwell 定理说明对任意平方可积估计量 ",[1840,4015,4017,4031],{"className":4016},[1843],[1840,4018,4020],{"className":4019},[1847],[1849,4021,4022],{"xmlns":1851},[1853,4023,4024,4029],{},[1856,4025,4026],{},[1863,4027,4028],{},"U",[1909,4030,4028],{"encoding":1911},[1840,4032,4034],{"className":4033,"ariaHidden":1861},[1916],[1840,4035,4037,4040],{"className":4036},[1920],[1840,4038],{"className":4039,"style":3733},[1924],[1840,4041,4028],{"className":4042,"style":3563},[1929,1954],"，",[1840,4045,4047],{"className":4046},[2132],[1840,4048,4050,4075],{"className":4049},[1843],[1840,4051,4053],{"className":4052},[1847],[1849,4054,4055],{"xmlns":1851,"display":2141},[1853,4056,4057,4072],{},[1856,4058,4059,4061,4063,4065,4068,4070],{},[1863,4060,2175],{},[1867,4062,2180],{"stretchy":1878},[1863,4064,4028],{},[1867,4066,4067],{},"∣",[1863,4069,1875],{},[1867,4071,2189],{"stretchy":1878},[1909,4073,4074],{"encoding":1911},"E[U\\mid T]",[1840,4076,4078,4102],{"className":4077,"ariaHidden":1861},[1916],[1840,4079,4081,4084,4087,4090,4093,4096,4099],{"className":4080},[1920],[1840,4082],{"className":4083,"style":1997},[1924],[1840,4085,2175],{"className":4086,"style":2317},[1929,1954],[1840,4088,2180],{"className":4089},[2005],[1840,4091,4028],{"className":4092,"style":3563},[1929,1954],[1840,4094],{"className":4095,"style":1983},[1982],[1840,4097,4067],{"className":4098},[1987],[1840,4100],{"className":4101,"style":1983},[1982],[1840,4103,4105,4108,4111],{"className":4104},[1920],[1840,4106],{"className":4107,"style":1997},[1924],[1840,4109,1875],{"className":4110,"style":2001},[1929,1954],[1840,4112,2189],{"className":4113},[2124],[1796,4115,4116,4117,4145],{},"在保持期望的同时，方差不大于 ",[1840,4118,4120,4133],{"className":4119},[1843],[1840,4121,4123],{"className":4122},[1847],[1849,4124,4125],{"xmlns":1851},[1853,4126,4127,4131],{},[1856,4128,4129],{},[1863,4130,4028],{},[1909,4132,4028],{"encoding":1911},[1840,4134,4136],{"className":4135,"ariaHidden":1861},[1916],[1840,4137,4139,4142],{"className":4138},[1920],[1840,4140],{"className":4141,"style":3733},[1924],[1840,4143,4028],{"className":4144,"style":3563},[1929,1954],"。这把“利用全部信息”变成可证明的改进。",[1807,4147,4149],{"id":4148},"_4-cramérrao-下界","4. Cramér–Rao 下界",[1796,4151,4152],{},"在正则条件下，无偏估计量满足：",[1840,4154,4156],{"className":4155},[2132],[1840,4157,4159,4216],{"className":4158},[1843],[1840,4160,4162],{"className":4161},[1847],[1849,4163,4164],{"xmlns":1851,"display":2141},[1853,4165,4166,4213],{},[1856,4167,4168,4178,4180,4186,4188,4191,4211],{},[1881,4169,4170,4176],{},[1856,4171,4172,4174],{},[1863,4173,2494],{"mathvariant":2152},[1867,4175,2156],{},[1863,4177,1865],{},[1867,4179,1879],{"stretchy":1878},[1859,4181,4182,4184],{"accent":1861},[1863,4183,1865],{},[1867,4185,1869],{"stretchy":1861},[1867,4187,1907],{"stretchy":1878},[1867,4189,4190],{},"≥",[4192,4193,4194,4196],"mfrac",{},[1887,4195,1889],{},[1856,4197,4198,4205,4207,4209],{},[1881,4199,4200,4203],{},[1863,4201,4202],{},"I",[1863,4204,1904],{},[1867,4206,1879],{"stretchy":1878},[1863,4208,1865],{},[1867,4210,1907],{"stretchy":1878},[1867,4212,1892],{"separator":1861},[1909,4214,4215],{"encoding":1911},"\\operatorname{Var}_\\theta(\\widehat\\theta)\n\\ge\\frac{1}{I_n(\\theta)},",[1840,4217,4219,4315],{"className":4218,"ariaHidden":1861},[1916],[1840,4220,4222,4225,4268,4271,4303,4306,4309,4312],{"className":4221},[1920],[1840,4223],{"className":4224,"style":2210},[1924],[1840,4226,4228,4234],{"className":4227},[2214],[1840,4229,4231],{"className":4230},[2214],[1840,4232,2494],{"className":4233},[1929,2221],[1840,4235,4237],{"className":4236},[2016],[1840,4238,4240,4260],{"className":4239},[1934,2020],[1840,4241,4243,4257],{"className":4242},[1938],[1840,4244,4246],{"className":4245,"style":2234},[1942],[1840,4247,4248,4251],{"style":2237},[1840,4249],{"className":4250,"style":2034},[1949],[1840,4252,4254],{"className":4253},[2038,2039,2040,2041],[1840,4255,1865],{"className":4256,"style":1955},[1929,1954,2041],[1840,4258,2049],{"className":4259},[2048],[1840,4261,4263],{"className":4262},[1938],[1840,4264,4266],{"className":4265,"style":2056},[1942],[1840,4267],{},[1840,4269,1879],{"className":4270},[2005],[1840,4272,4274],{"className":4273},[1929,1930],[1840,4275,4277],{"className":4276},[1934],[1840,4278,4280],{"className":4279},[1938],[1840,4281,4283,4291],{"className":4282,"style":1925},[1942],[1840,4284,4285,4288],{"style":1945},[1840,4286],{"className":4287,"style":1950},[1949],[1840,4289,1865],{"className":4290,"style":1955},[1929,1954],[1840,4292,4294,4297],{"className":4293,"style":1960},[1959],[1840,4295],{"className":4296,"style":1950},[1949],[1840,4298,4299],{"style":1966},[1968,4300,4301],{"xmlns":1970,"width":1971,"height":1972,"viewBox":1973,"preserveAspectRatio":1974},[1976,4302],{"d":1978},[1840,4304,1907],{"className":4305},[2124],[1840,4307],{"className":4308,"style":1983},[1982],[1840,4310,4190],{"className":4311},[1987],[1840,4313],{"className":4314,"style":1983},[1982],[1840,4316,4318,4322,4438],{"className":4317},[1920],[1840,4319],{"className":4320,"style":4321},[1924],"height:2.2574em;vertical-align:-0.936em;",[1840,4323,4325,4329,4435],{"className":4324},[1929],[1840,4326],{"className":4327},[2005,4328],"nulldelimiter",[1840,4330,4332],{"className":4331},[4192],[1840,4333,4335,4426],{"className":4334},[1934,2020],[1840,4336,4338,4423],{"className":4337},[1938],[1840,4339,4342,4400,4411],{"className":4340,"style":4341},[1942],"height:1.3214em;",[1840,4343,4345,4348],{"style":4344},"top:-2.314em;",[1840,4346],{"className":4347,"style":1950},[1949],[1840,4349,4351,4391,4394,4397],{"className":4350},[1929],[1840,4352,4354,4357],{"className":4353},[1929],[1840,4355,4202],{"className":4356,"style":2012},[1929,1954],[1840,4358,4360],{"className":4359},[2016],[1840,4361,4363,4383],{"className":4362},[1934,2020],[1840,4364,4366,4380],{"className":4365},[1938],[1840,4367,4369],{"className":4368,"style":2098},[1942],[1840,4370,4371,4374],{"style":2030},[1840,4372],{"className":4373,"style":2034},[1949],[1840,4375,4377],{"className":4376},[2038,2039,2040,2041],[1840,4378,1904],{"className":4379},[1929,1954,2041],[1840,4381,2049],{"className":4382},[2048],[1840,4384,4386],{"className":4385},[1938],[1840,4387,4389],{"className":4388,"style":2056},[1942],[1840,4390],{},[1840,4392,1879],{"className":4393},[2005],[1840,4395,1865],{"className":4396,"style":1955},[1929,1954],[1840,4398,1907],{"className":4399},[2124],[1840,4401,4403,4406],{"style":4402},"top:-3.23em;",[1840,4404],{"className":4405,"style":1950},[1949],[1840,4407],{"className":4408,"style":4410},[4409],"frac-line","border-bottom-width:0.04em;",[1840,4412,4414,4417],{"style":4413},"top:-3.677em;",[1840,4415],{"className":4416,"style":1950},[1949],[1840,4418,4420],{"className":4419},[1929],[1840,4421,1889],{"className":4422},[1929],[1840,4424,2049],{"className":4425},[2048],[1840,4427,4429],{"className":4428},[1938],[1840,4430,4433],{"className":4431,"style":4432},[1942],"height:0.936em;",[1840,4434],{},[1840,4436],{"className":4437},[2124,4328],[1840,4439,1892],{"className":4440},[2062],[1796,4442,4443],{},"其中 Fisher 信息",[1840,4445,4447],{"className":4446},[2132],[1840,4448,4450,4530],{"className":4449},[1843],[1840,4451,4453],{"className":4452},[1847],[1849,4454,4455],{"xmlns":1851,"display":2141},[1853,4456,4457,4527],{},[1856,4458,4459,4465,4467,4469,4471,4473,4479,4525],{},[1881,4460,4461,4463],{},[1863,4462,4202],{},[1863,4464,1904],{},[1867,4466,1879],{"stretchy":1878},[1863,4468,1865],{},[1867,4470,1907],{"stretchy":1878},[1867,4472,1872],{},[1881,4474,4475,4477],{},[1863,4476,2175],{},[1863,4478,1865],{},[1856,4480,4481,4483,4523],{},[1867,4482,2180],{"fence":1861},[2477,4484,4485,4521],{},[1856,4486,4487,4489,4500,4503,4505,4508,4510,4512,4515,4517,4519],{},[1867,4488,1879],{"fence":1861},[4192,4490,4491,4494],{},[1863,4492,4493],{"mathvariant":2152},"∂",[1856,4495,4496,4498],{},[1863,4497,4493],{"mathvariant":2152},[1863,4499,1865],{},[1863,4501,4502],{},"log",[1867,4504,2156],{},[1863,4506,4507],{},"L",[1867,4509,1879],{"stretchy":1878},[1863,4511,1865],{},[1867,4513,4514],{"separator":1861},";",[1863,4516,1885],{},[1867,4518,1907],{"stretchy":1878},[1867,4520,1907],{"fence":1861},[1887,4522,2483],{},[1867,4524,2189],{"fence":1861},[1863,4526,2197],{"mathvariant":2152},[1909,4528,4529],{"encoding":1911},"I_n(\\theta)\n=E_\\theta\\left[\n\\left(\\frac{\\partial}{\\partial\\theta}\\log L(\\theta;X)\\right)^2\n\\right].",[1840,4531,4533,4597],{"className":4532,"ariaHidden":1861},[1916],[1840,4534,4536,4539,4579,4582,4585,4588,4591,4594],{"className":4535},[1920],[1840,4537],{"className":4538,"style":1997},[1924],[1840,4540,4542,4545],{"className":4541},[1929],[1840,4543,4202],{"className":4544,"style":2012},[1929,1954],[1840,4546,4548],{"className":4547},[2016],[1840,4549,4551,4571],{"className":4550},[1934,2020],[1840,4552,4554,4568],{"className":4553},[1938],[1840,4555,4557],{"className":4556,"style":2098},[1942],[1840,4558,4559,4562],{"style":2030},[1840,4560],{"className":4561,"style":2034},[1949],[1840,4563,4565],{"className":4564},[2038,2039,2040,2041],[1840,4566,1904],{"className":4567},[1929,1954,2041],[1840,4569,2049],{"className":4570},[2048],[1840,4572,4574],{"className":4573},[1938],[1840,4575,4577],{"className":4576,"style":2056},[1942],[1840,4578],{},[1840,4580,1879],{"className":4581},[2005],[1840,4583,1865],{"className":4584,"style":1955},[1929,1954],[1840,4586,1907],{"className":4587},[2124],[1840,4589],{"className":4590,"style":1983},[1982],[1840,4592,1872],{"className":4593},[1987],[1840,4595],{"className":4596,"style":1983},[1982],[1840,4598,4600,4604,4644,4647,4811,4814],{"className":4599},[1920],[1840,4601],{"className":4602,"style":4603},[1924],"height:3em;vertical-align:-1.25em;",[1840,4605,4607,4610],{"className":4606},[1929],[1840,4608,2175],{"className":4609,"style":2317},[1929,1954],[1840,4611,4613],{"className":4612},[2016],[1840,4614,4616,4636],{"className":4615},[1934,2020],[1840,4617,4619,4633],{"className":4618},[1938],[1840,4620,4622],{"className":4621,"style":2234},[1942],[1840,4623,4624,4627],{"style":2332},[1840,4625],{"className":4626,"style":2034},[1949],[1840,4628,4630],{"className":4629},[2038,2039,2040,2041],[1840,4631,1865],{"className":4632,"style":1955},[1929,1954,2041],[1840,4634,2049],{"className":4635},[2048],[1840,4637,4639],{"className":4638},[1938],[1840,4640,4642],{"className":4641,"style":2056},[1942],[1840,4643],{},[1840,4645],{"className":4646,"style":2066},[1982],[1840,4648,4650,4660,4805],{"className":4649},[2070],[1840,4651,4655],{"className":4652,"style":4654},[2005,4653],"delimcenter","top:0em;",[1840,4656,2180],{"className":4657},[4658,4659],"delimsizing","size4",[1840,4661,4663,4780],{"className":4662},[2070],[1840,4664,4666,4672,4740,4743,4750,4753,4756,4759,4762,4765,4768,4771,4774],{"className":4665},[2070],[1840,4667,4669],{"className":4668,"style":4654},[2005,4653],[1840,4670,1879],{"className":4671},[4658,2040],[1840,4673,4675,4678,4737],{"className":4674},[1929],[1840,4676],{"className":4677},[2005,4328],[1840,4679,4681],{"className":4680},[4192],[1840,4682,4684,4728],{"className":4683},[1934,2020],[1840,4685,4687,4725],{"className":4686},[1938],[1840,4688,4691,4706,4714],{"className":4689,"style":4690},[1942],"height:1.3714em;",[1840,4692,4693,4696],{"style":4344},[1840,4694],{"className":4695,"style":1950},[1949],[1840,4697,4699,4703],{"className":4698},[1929],[1840,4700,4493],{"className":4701,"style":4702},[1929],"margin-right:0.0556em;",[1840,4704,1865],{"className":4705,"style":1955},[1929,1954],[1840,4707,4708,4711],{"style":4402},[1840,4709],{"className":4710,"style":1950},[1949],[1840,4712],{"className":4713,"style":4410},[4409],[1840,4715,4716,4719],{"style":4413},[1840,4717],{"className":4718,"style":1950},[1949],[1840,4720,4722],{"className":4721},[1929],[1840,4723,4493],{"className":4724,"style":4702},[1929],[1840,4726,2049],{"className":4727},[2048],[1840,4729,4731],{"className":4730},[1938],[1840,4732,4735],{"className":4733,"style":4734},[1942],"height:0.686em;",[1840,4736],{},[1840,4738],{"className":4739},[2124,4328],[1840,4741],{"className":4742,"style":2066},[1982],[1840,4744,4746,4747],{"className":4745},[2214],"lo",[1840,4748,3805],{"style":4749},"margin-right:0.0139em;",[1840,4751],{"className":4752,"style":2066},[1982],[1840,4754,4507],{"className":4755},[1929,1954],[1840,4757,1879],{"className":4758},[2005],[1840,4760,1865],{"className":4761,"style":1955},[1929,1954],[1840,4763,4514],{"className":4764},[2062],[1840,4766],{"className":4767,"style":2066},[1982],[1840,4769,1885],{"className":4770,"style":2012},[1929,1954],[1840,4772,1907],{"className":4773},[2124],[1840,4775,4777],{"className":4776,"style":4654},[2124,4653],[1840,4778,1907],{"className":4779},[4658,2040],[1840,4781,4783],{"className":4782},[2016],[1840,4784,4786],{"className":4785},[1934],[1840,4787,4789],{"className":4788},[1938],[1840,4790,4793],{"className":4791,"style":4792},[1942],"height:1.654em;",[1840,4794,4796,4799],{"style":4795},"top:-3.9029em;margin-right:0.05em;",[1840,4797],{"className":4798,"style":2034},[1949],[1840,4800,4802],{"className":4801},[2038,2039,2040,2041],[1840,4803,2483],{"className":4804},[1929,2041],[1840,4806,4808],{"className":4807,"style":4654},[2124,4653],[1840,4809,2189],{"className":4810},[4658,4659],[1840,4812],{"className":4813,"style":2066},[1982],[1840,4815,2197],{"className":4816},[1929],[1796,4818,4819],{},"达到下界称为有效。边界参数、支持集依赖参数或非正则模型可能不满足经典条件；不能只看公式形式。",[1807,4821,4823],{"id":4822},"_5-稳健性模型近似错误时会怎样","5. 稳健性：模型近似错误时会怎样",[1796,4825,4826],{},"常用概念：",[4828,4829,4830,4833,4836,4839],"ul",{},[1817,4831,4832],{},"影响函数：单个微小污染对估计的局部影响；",[1817,4834,4835],{},"breakdown point：多大比例污染可使估计任意失真；",[1817,4837,4838],{},"截尾\u002FHuber 损失：限制极端观测影响；",[1817,4840,4841],{},"sandwich 方差：允许部分方差模型错误。",[1796,4843,4844],{},"稳健通常以效率为代价；应在理想模型性能与合理污染风险之间权衡。",[1807,4846,4848],{"id":4847},"_6-可运行案例均值与-10-截尾均值","6. 可运行案例：均值与 10% 截尾均值",[1796,4850,4851],{},"代码比较两种世界：纯正态与 5% 对称极端污染。目标中心均为 0。",[4853,4854],"pyodide",{"code64":4855,"layout":4856,"locale":7,"packages":4857,"title":4858},"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","vertical","numpy","Python：效率与稳健性的权衡",[1796,4860,4861],{},"在纯正态模型中，样本均值方差最小；污染下，少数极端值大幅抬高其 MSE。没有脱离模型与损失的“永远最佳”估计量。",[1807,4863,4865],{"id":4864},"_7-决策论视角","7. 决策论视角",[1796,4867,4868,4869,4927,4928,4974],{},"给定损失 ",[1840,4870,4872,4897],{"className":4871},[1843],[1840,4873,4875],{"className":4874},[1847],[1849,4876,4877],{"xmlns":1851},[1853,4878,4879,4894],{},[1856,4880,4881,4883,4885,4887,4889,4892],{},[1863,4882,4507],{},[1867,4884,1879],{"stretchy":1878},[1863,4886,1865],{},[1867,4888,1892],{"separator":1861},[1863,4890,4891],{},"a",[1867,4893,1907],{"stretchy":1878},[1909,4895,4896],{"encoding":1911},"L(\\theta,a)",[1840,4898,4900],{"className":4899,"ariaHidden":1861},[1916],[1840,4901,4903,4906,4909,4912,4915,4918,4921,4924],{"className":4902},[1920],[1840,4904],{"className":4905,"style":1997},[1924],[1840,4907,4507],{"className":4908},[1929,1954],[1840,4910,1879],{"className":4911},[2005],[1840,4913,1865],{"className":4914,"style":1955},[1929,1954],[1840,4916,1892],{"className":4917},[2062],[1840,4919],{"className":4920,"style":2066},[1982],[1840,4922,4891],{"className":4923},[1929,1954],[1840,4925,1907],{"className":4926},[2124],"，估计规则 ",[1840,4929,4931,4952],{"className":4930},[1843],[1840,4932,4934],{"className":4933},[1847],[1849,4935,4936],{"xmlns":1851},[1853,4937,4938,4949],{},[1856,4939,4940,4943,4945,4947],{},[1863,4941,4942],{},"δ",[1867,4944,1879],{"stretchy":1878},[1863,4946,1885],{},[1867,4948,1907],{"stretchy":1878},[1909,4950,4951],{"encoding":1911},"\\delta(X)",[1840,4953,4955],{"className":4954,"ariaHidden":1861},[1916],[1840,4956,4958,4961,4965,4968,4971],{"className":4957},[1920],[1840,4959],{"className":4960,"style":1997},[1924],[1840,4962,4942],{"className":4963,"style":4964},[1929,1954],"margin-right:0.0379em;",[1840,4966,1879],{"className":4967},[2005],[1840,4969,1885],{"className":4970,"style":2012},[1929,1954],[1840,4972,1907],{"className":4973},[2124]," 的风险：",[1840,4976,4978],{"className":4977},[2132],[1840,4979,4981,5038],{"className":4980},[1843],[1840,4982,4984],{"className":4983},[1847],[1849,4985,4986],{"xmlns":1851,"display":2141},[1853,4987,4988,5035],{},[1856,4989,4990,4993,4995,4997,4999,5001,5003,5005,5011,5013,5015,5017,5019,5021,5023,5025,5027,5029,5031,5033],{},[1863,4991,4992],{},"R",[1867,4994,1879],{"stretchy":1878},[1863,4996,1865],{},[1867,4998,1892],{"separator":1861},[1863,5000,4942],{},[1867,5002,1907],{"stretchy":1878},[1867,5004,1872],{},[1881,5006,5007,5009],{},[1863,5008,2175],{},[1863,5010,1865],{},[1867,5012,2180],{"stretchy":1878},[1863,5014,4507],{},[1867,5016,1879],{"stretchy":1878},[1863,5018,1865],{},[1867,5020,1892],{"separator":1861},[1863,5022,4942],{},[1867,5024,1879],{"stretchy":1878},[1863,5026,1885],{},[1867,5028,1907],{"stretchy":1878},[1867,5030,1907],{"stretchy":1878},[1867,5032,2189],{"stretchy":1878},[1863,5034,2197],{"mathvariant":2152},[1909,5036,5037],{"encoding":1911},"R(\\theta,\\delta)\n=E_\\theta[L(\\theta,\\delta(X))].",[1840,5039,5041,5078],{"className":5040,"ariaHidden":1861},[1916],[1840,5042,5044,5047,5051,5054,5057,5060,5063,5066,5069,5072,5075],{"className":5043},[1920],[1840,5045],{"className":5046,"style":1997},[1924],[1840,5048,4992],{"className":5049,"style":5050},[1929,1954],"margin-right:0.0077em;",[1840,5052,1879],{"className":5053},[2005],[1840,5055,1865],{"className":5056,"style":1955},[1929,1954],[1840,5058,1892],{"className":5059},[2062],[1840,5061],{"className":5062,"style":2066},[1982],[1840,5064,4942],{"className":5065,"style":4964},[1929,1954],[1840,5067,1907],{"className":5068},[2124],[1840,5070],{"className":5071,"style":1983},[1982],[1840,5073,1872],{"className":5074},[1987],[1840,5076],{"className":5077,"style":1983},[1982],[1840,5079,5081,5084,5124,5127,5130,5133,5136,5139,5142,5145,5148,5151,5155],{"className":5080},[1920],[1840,5082],{"className":5083,"style":1997},[1924],[1840,5085,5087,5090],{"className":5086},[1929],[1840,5088,2175],{"className":5089,"style":2317},[1929,1954],[1840,5091,5093],{"className":5092},[2016],[1840,5094,5096,5116],{"className":5095},[1934,2020],[1840,5097,5099,5113],{"className":5098},[1938],[1840,5100,5102],{"className":5101,"style":2234},[1942],[1840,5103,5104,5107],{"style":2332},[1840,5105],{"className":5106,"style":2034},[1949],[1840,5108,5110],{"className":5109},[2038,2039,2040,2041],[1840,5111,1865],{"className":5112,"style":1955},[1929,1954,2041],[1840,5114,2049],{"className":5115},[2048],[1840,5117,5119],{"className":5118},[1938],[1840,5120,5122],{"className":5121,"style":2056},[1942],[1840,5123],{},[1840,5125,2180],{"className":5126},[2005],[1840,5128,4507],{"className":5129},[1929,1954],[1840,5131,1879],{"className":5132},[2005],[1840,5134,1865],{"className":5135,"style":1955},[1929,1954],[1840,5137,1892],{"className":5138},[2062],[1840,5140],{"className":5141,"style":2066},[1982],[1840,5143,4942],{"className":5144,"style":4964},[1929,1954],[1840,5146,1879],{"className":5147},[2005],[1840,5149,1885],{"className":5150,"style":2012},[1929,1954],[1840,5152,5154],{"className":5153},[2124],"))]",[1840,5156,2197],{"className":5157},[1929],[4828,5159,5160,5163,5166],{},[1817,5161,5162],{},"平方损失对应均值与 MSE；",[1817,5164,5165],{},"绝对损失对应中位数；",[1817,5167,5168],{},"非对称损失适合漏报和误报成本不同的决策。",[1796,5170,5171],{},"Bayes、minimax 与可容许性都建立在风险比较上，不能仅凭无偏性决定。",[1807,5173,5175],{"id":5174},"_8-诊断清单","8. 诊断清单",[4828,5177,5178,5181,5184,5187,5190,5193,5196],{},[1817,5179,5180],{},"目标参数与损失函数是什么？",[1817,5182,5183],{},"比较的是有限样本还是渐近性质？",[1817,5185,5186],{},"偏差、方差与 MSE 是否同时报告？",[1817,5188,5189],{},"正则条件与参数边界是否满足？",[1817,5191,5192],{},"充分统计量是否存在？",[1817,5194,5195],{},"离群点是数据错误、混合人群还是真实重尾？",[1817,5197,5198],{},"稳健方法改变了哪个 estimand？",[1807,5200,5201],{"id":5201},"课堂任务",[1796,5203,5204,5205,5362],{},"对 ",[1840,5206,5208,5260],{"className":5207},[1843],[1840,5209,5211],{"className":5210},[1847],[1849,5212,5213],{"xmlns":1851},[1853,5214,5215,5257],{},[1856,5216,5217,5224,5227,5230,5233,5236,5238,5241,5244,5247,5249,5251,5253,5255],{},[1881,5218,5219,5221],{},[1863,5220,1885],{},[1863,5222,5223],{},"i",[1867,5225,5226],{},"∼",[1863,5228,5229],{},"B",[1863,5231,5232],{},"e",[1863,5234,5235],{},"r",[1863,5237,1904],{},[1863,5239,5240],{},"o",[1863,5242,5243],{},"u",[1863,5245,5246],{},"l",[1863,5248,5246],{},[1863,5250,5223],{},[1867,5252,1879],{"stretchy":1878},[1863,5254,1796],{},[1867,5256,1907],{"stretchy":1878},[1909,5258,5259],{"encoding":1911},"X_i\\sim Bernoulli(p)",[1840,5261,5263,5320],{"className":5262,"ariaHidden":1861},[1916],[1840,5264,5266,5270,5311,5314,5317],{"className":5265},[1920],[1840,5267],{"className":5268,"style":5269},[1924],"height:0.8333em;vertical-align:-0.15em;",[1840,5271,5273,5276],{"className":5272},[1929],[1840,5274,1885],{"className":5275,"style":2012},[1929,1954],[1840,5277,5279],{"className":5278},[2016],[1840,5280,5282,5303],{"className":5281},[1934,2020],[1840,5283,5285,5300],{"className":5284},[1938],[1840,5286,5289],{"className":5287,"style":5288},[1942],"height:0.3117em;",[1840,5290,5291,5294],{"style":2030},[1840,5292],{"className":5293,"style":2034},[1949],[1840,5295,5297],{"className":5296},[2038,2039,2040,2041],[1840,5298,5223],{"className":5299},[1929,1954,2041],[1840,5301,2049],{"className":5302},[2048],[1840,5304,5306],{"className":5305},[1938],[1840,5307,5309],{"className":5308,"style":2056},[1942],[1840,5310],{},[1840,5312],{"className":5313,"style":1983},[1982],[1840,5315,5226],{"className":5316},[1987],[1840,5318],{"className":5319,"style":1983},[1982],[1840,5321,5323,5326,5330,5334,5337,5340,5343,5347,5350,5353,5356,5359],{"className":5322},[1920],[1840,5324],{"className":5325,"style":1997},[1924],[1840,5327,5229],{"className":5328,"style":5329},[1929,1954],"margin-right:0.0502em;",[1840,5331,5333],{"className":5332,"style":1955},[1929,1954],"er",[1840,5335,1904],{"className":5336},[1929,1954],[1840,5338,5240],{"className":5339},[1929,1954],[1840,5341,5243],{"className":5342},[1929,1954],[1840,5344,5246],{"className":5345,"style":5346},[1929,1954],"margin-right:0.0197em;",[1840,5348,5246],{"className":5349,"style":5346},[1929,1954],[1840,5351,5223],{"className":5352},[1929,1954],[1840,5354,1879],{"className":5355},[2005],[1840,5357,1796],{"className":5358},[1929,1954],[1840,5360,1907],{"className":5361},[2124],"：",[1814,5364,5365,5435,5595,5598],{},[1817,5366,5367,5368,5434],{},"证明 ",[1840,5369,5371,5390],{"className":5370},[1843],[1840,5372,5374],{"className":5373},[1847],[1849,5375,5376],{"xmlns":1851},[1853,5377,5378,5387],{},[1856,5379,5380],{},[1859,5381,5382,5384],{"accent":1861},[1863,5383,1885],{},[1867,5385,5386],{},"ˉ",[1909,5388,5389],{"encoding":1911},"\\bar X",[1840,5391,5393],{"className":5392,"ariaHidden":1861},[1916],[1840,5394,5396,5400],{"className":5395},[1920],[1840,5397],{"className":5398,"style":5399},[1924],"height:0.8201em;",[1840,5401,5403],{"className":5402},[1929,1930],[1840,5404,5406],{"className":5405},[1934],[1840,5407,5409],{"className":5408},[1938],[1840,5410,5412,5420],{"className":5411,"style":5399},[1942],[1840,5413,5414,5417],{"style":1945},[1840,5415],{"className":5416,"style":1950},[1949],[1840,5418,1885],{"className":5419,"style":2012},[1929,1954],[1840,5421,5423,5426],{"style":5422},"top:-3.2523em;",[1840,5424],{"className":5425,"style":1950},[1949],[1840,5427,5431],{"className":5428,"style":5430},[5429],"accent-body","left:-0.1667em;",[1840,5432,5386],{"className":5433},[1929]," 无偏并计算 MSE；",[1817,5436,5437,5438,3677,5565,5594],{},"说明 ",[1840,5439,5441,5466],{"className":5440},[1843],[1840,5442,5444],{"className":5443},[1847],[1849,5445,5446],{"xmlns":1851},[1853,5447,5448,5463],{},[1856,5449,5450,5457],{},[1881,5451,5452,5455],{},[1867,5453,5454],{},"∑",[1863,5456,5223],{},[1881,5458,5459,5461],{},[1863,5460,1885],{},[1863,5462,5223],{},[1909,5464,5465],{"encoding":1911},"\\sum_iX_i",[1840,5467,5469],{"className":5468,"ariaHidden":1861},[1916],[1840,5470,5472,5476,5522,5525],{"className":5471},[1920],[1840,5473],{"className":5474,"style":5475},[1924],"height:1.0497em;vertical-align:-0.2997em;",[1840,5477,5479,5485],{"className":5478},[2214],[1840,5480,5454],{"className":5481,"style":5484},[2214,5482,5483],"op-symbol","small-op","position:relative;top:0em;",[1840,5486,5488],{"className":5487},[2016],[1840,5489,5491,5513],{"className":5490},[1934,2020],[1840,5492,5494,5510],{"className":5493},[1938],[1840,5495,5498],{"className":5496,"style":5497},[1942],"height:0.162em;",[1840,5499,5501,5504],{"style":5500},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1840,5502],{"className":5503,"style":2034},[1949],[1840,5505,5507],{"className":5506},[2038,2039,2040,2041],[1840,5508,5223],{"className":5509},[1929,1954,2041],[1840,5511,2049],{"className":5512},[2048],[1840,5514,5516],{"className":5515},[1938],[1840,5517,5520],{"className":5518,"style":5519},[1942],"height:0.2997em;",[1840,5521],{},[1840,5523],{"className":5524,"style":2066},[1982],[1840,5526,5528,5531],{"className":5527},[1929],[1840,5529,1885],{"className":5530,"style":2012},[1929,1954],[1840,5532,5534],{"className":5533},[2016],[1840,5535,5537,5557],{"className":5536},[1934,2020],[1840,5538,5540,5554],{"className":5539},[1938],[1840,5541,5543],{"className":5542,"style":5288},[1942],[1840,5544,5545,5548],{"style":2030},[1840,5546],{"className":5547,"style":2034},[1949],[1840,5549,5551],{"className":5550},[2038,2039,2040,2041],[1840,5552,5223],{"className":5553},[1929,1954,2041],[1840,5555,2049],{"className":5556},[2048],[1840,5558,5560],{"className":5559},[1938],[1840,5561,5563],{"className":5562,"style":2056},[1942],[1840,5564],{},[1840,5566,5568,5581],{"className":5567},[1843],[1840,5569,5571],{"className":5570},[1847],[1849,5572,5573],{"xmlns":1851},[1853,5574,5575,5579],{},[1856,5576,5577],{},[1863,5578,1796],{},[1909,5580,1796],{"encoding":1911},[1840,5582,5584],{"className":5583,"ariaHidden":1861},[1916],[1840,5585,5587,5591],{"className":5586},[1920],[1840,5588],{"className":5589,"style":5590},[1924],"height:0.625em;vertical-align:-0.1944em;",[1840,5592,1796],{"className":5593},[1929,1954]," 充分；",[1817,5596,5597],{},"推导 Fisher 信息与 CRLB；",[1817,5599,5600,5601,5661,5662,5815],{},"比较 ",[1840,5602,5604,5621],{"className":5603},[1843],[1840,5605,5607],{"className":5606},[1847],[1849,5608,5609],{"xmlns":1851},[1853,5610,5611,5619],{},[1856,5612,5613],{},[1859,5614,5615,5617],{"accent":1861},[1863,5616,1885],{},[1867,5618,5386],{},[1909,5620,5389],{"encoding":1911},[1840,5622,5624],{"className":5623,"ariaHidden":1861},[1916],[1840,5625,5627,5630],{"className":5626},[1920],[1840,5628],{"className":5629,"style":5399},[1924],[1840,5631,5633],{"className":5632},[1929,1930],[1840,5634,5636],{"className":5635},[1934],[1840,5637,5639],{"className":5638},[1938],[1840,5640,5642,5650],{"className":5641,"style":5399},[1942],[1840,5643,5644,5647],{"style":1945},[1840,5645],{"className":5646,"style":1950},[1949],[1840,5648,1885],{"className":5649,"style":2012},[1929,1954],[1840,5651,5652,5655],{"style":5422},[1840,5653],{"className":5654,"style":1950},[1949],[1840,5656,5658],{"className":5657,"style":5430},[5429],[1840,5659,5386],{"className":5660},[1929]," 与 ",[1840,5663,5665,5706],{"className":5664},[1843],[1840,5666,5668],{"className":5667},[1847],[1849,5669,5670],{"xmlns":1851},[1853,5671,5672,5703],{},[1856,5673,5674,5676,5678,5684,5686,5688,5690,5693,5695,5697,5699,5701],{},[1867,5675,1879],{"stretchy":1878},[1867,5677,5454],{},[1881,5679,5680,5682],{},[1863,5681,1885],{},[1863,5683,5223],{},[1867,5685,2511],{},[1887,5687,1889],{},[1867,5689,1907],{"stretchy":1878},[1863,5691,5692],{"mathvariant":2152},"\u002F",[1867,5694,1879],{"stretchy":1878},[1863,5696,1904],{},[1867,5698,2511],{},[1887,5700,2483],{},[1867,5702,1907],{"stretchy":1878},[1909,5704,5705],{"encoding":1911},"(\\sum X_i+1)\u002F(n+2)",[1840,5707,5709,5773,5803],{"className":5708,"ariaHidden":1861},[1916],[1840,5710,5712,5715,5718,5721,5724,5764,5767,5770],{"className":5711},[1920],[1840,5713],{"className":5714,"style":1997},[1924],[1840,5716,1879],{"className":5717},[2005],[1840,5719,5454],{"className":5720,"style":5484},[2214,5482,5483],[1840,5722],{"className":5723,"style":2066},[1982],[1840,5725,5727,5730],{"className":5726},[1929],[1840,5728,1885],{"className":5729,"style":2012},[1929,1954],[1840,5731,5733],{"className":5732},[2016],[1840,5734,5736,5756],{"className":5735},[1934,2020],[1840,5737,5739,5753],{"className":5738},[1938],[1840,5740,5742],{"className":5741,"style":5288},[1942],[1840,5743,5744,5747],{"style":2030},[1840,5745],{"className":5746,"style":2034},[1949],[1840,5748,5750],{"className":5749},[2038,2039,2040,2041],[1840,5751,5223],{"className":5752},[1929,1954,2041],[1840,5754,2049],{"className":5755},[2048],[1840,5757,5759],{"className":5758},[1938],[1840,5760,5762],{"className":5761,"style":2056},[1942],[1840,5763],{},[1840,5765],{"className":5766,"style":2394},[1982],[1840,5768,2511],{"className":5769},[2398],[1840,5771],{"className":5772,"style":2394},[1982],[1840,5774,5776,5779,5782,5785,5788,5791,5794,5797,5800],{"className":5775},[1920],[1840,5777],{"className":5778,"style":1997},[1924],[1840,5780,1889],{"className":5781},[1929],[1840,5783,1907],{"className":5784},[2124],[1840,5786,5692],{"className":5787},[1929],[1840,5789,1879],{"className":5790},[2005],[1840,5792,1904],{"className":5793},[1929,1954],[1840,5795],{"className":5796,"style":2394},[1982],[1840,5798,2511],{"className":5799},[2398],[1840,5801],{"className":5802,"style":2394},[1982],[1840,5804,5806,5809,5812],{"className":5805},[1920],[1840,5807],{"className":5808,"style":1997},[1924],[1840,5810,2483],{"className":5811},[1929],[1840,5813,1907],{"className":5814},[2124]," 的偏差—方差。",[1807,5817,5818],{"id":5818},"核心阅读",[4828,5820,5821,5828,5835],{},[1817,5822,5823,5824,3766],{},"Lehmann & Casella, ",[5825,5826,5827],"em",{},"Theory of Point Estimation",[1817,5829,5830,5831,5834],{},"Casella & Berger, ",[5825,5832,5833],{},"Statistical Inference","，点估计理论章节。",[1817,5836,5837,5838,3766],{},"Huber & Ronchetti, ",[5825,5839,5840],{},"Robust Statistics",[1796,5842,5843,5844,5848,5849,3766],{},"上一章：",[4891,5845,5847],{"href":5846},"..\u002F02-interval-estimation\u002F","区间估计","｜下一章：",[4891,5850,5852],{"href":5851},"..\u002F04-pe-method\u002F","点估计方法",{"title":10,"searchDepth":5854,"depth":5854,"links":5855},2,[5856,5857,5858,5859,5860,5861,5862,5863,5864,5865,5866],{"id":1809,"depth":5854,"text":1809},{"id":1834,"depth":5854,"text":1835},{"id":3001,"depth":5854,"text":3002},{"id":3628,"depth":5854,"text":3629},{"id":4148,"depth":5854,"text":4149},{"id":4822,"depth":5854,"text":4823},{"id":4847,"depth":5854,"text":4848},{"id":4864,"depth":5854,"text":4865},{"id":5174,"depth":5854,"text":5175},{"id":5201,"depth":5854,"text":5201},{"id":5818,"depth":5854,"text":5818},"用偏差、方差、MSE、一致性、充分性、效率与稳健性评价估计量。","md",{"sidebar":5870},{"order":5871},9,true,{"title":1698,"description":5867},"DqlN2BmfTYZEa1JOrQ7IxVc3nbXMS0ge-IXUdc1bhCs",[5876,5878],{"title":1692,"path":1693,"stem":1694,"description":5877,"children":-1},"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。",{"title":1704,"path":1705,"stem":1706,"description":5879,"children":-1},"比较矩估计、极大似然、贝叶斯估计和 EM 算法的构造逻辑、计算与边界。",1785754757072]