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[美]邵 著 / 世界图书出版公司 / 2009-10 / 平装
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数理统计(第2版)
ProbabilityTheory、ProbabilitySpacesandRandomElements、σ-fieldsandmeasures、Measurablefunctionsanddistributions、IntegrationandDifferentiation、Integration、Radon.Nikodymderivative、DistributionsandTheirCharacteristics、Distributionsandprobabilitydensities、Momentsandmomentinequalities、Momentgeneratingandcharacteristicfunctions、onditionalExpectations、Conditionalexpectations、Independence、Conditionaldistributions、Markovchainsandmartingales、AsymptoticTheory、Convergencemodesandstochasticorders等等。
PrefacetotheFirstEditionPrefacetotheSecondEditionChapter1.ProbabilityTheory1.1ProbabilitySpacesandRandomElements1.1.1σ-fieldsandmeasures1.1.2Measurablefunctionsanddistributions1.2IntegrationandDifferentiation1.2.1Integration1.2.2Radon.Nikodymderivative1.3DistributionsandTheirCharacteristics1.3.1Distributionsandprobabilitydensities1.3.2Momentsandmomentinequalities1.3.3Momentgeneratingandcharacteristicfunctions1.4ConditionalExpectations1.4.1Conditionalexpectations1.4.2Independence1.4.3Conditionaldistributions1.4.4Markovchainsandmartingales1.5AsymptoticTheory1.5.1Convergencemodesandstochasticorders1.5.2Weakconvergence1.5.3Convergenceoftransformations1.5.4Thelawoflargenumbers1.5.5Thecentrallimittheorem1.5.6EdgeworthandCornish-Fisherexpansions1.6ExercisesChapter2.FundamentalsofStatistics2.1Populations,Samples,andModels2.1.1Populationsandsamples2.1.2Parametricandnonparametricmodels2.1.3Exponentialandlocation.scalefamilies2.2Statistics.Sufficiency,andCompleteness2.2.1Statisticsandtheirdistributions2.2.2Sufficiencyandminimalsufficiency2.2.3Completestatistics2.3StatisticalDecisionTheory2.3.1Decisionrules,lOSSfunctions,andrisks2.3.2Admissibilityandoptimality2.4StatisticalInference2.4.1P0il)testimators2.4.2Hypothesistests2.4.3Confidencesets2.5AsymptoticCriteriaandInference2.5.1Consistency2.5.2Asymptoticbias,variance,andmse2.5.3Asymptoticinference2.6ExercisesChapter3.UnbiasedEstimation3.1TheUMVUE3.1.1Sufficientandcompletestatistics3.1.2Anecessaryand.sufficientcondition3.1.3Informationinequality3.1.4AsymptoticpropertiesofUMVUEs3.2U-Statistics3.2.1Someexamples3.2.2VariancesofU-statistics3.2.3Theprojectionmethod3.3TheLSEinLinearModels3.3.1TheLSEandestimability3.3.2TheUMVUEandBLUE3.3.3R0bustnessofLSEs3.3.4AsymptoticpropertiesofLSEs3.4UnbiasedEstimatorsinSurveyProblems3.4.1UMVUEsofpopulationtotals3.4.2Horvitz-Thompsonestimators3.5AsymptoticallyUnbiasedEstimators3.5.1Functionsofunbiasedestimators3.5.2Themethodofmoments3.5.3V-statistics3.5.4TheweightedLSE3.6ExercisesChapter4.EstimationinParametricModels4.1BayesDecisionsandEstimators4.1.1Bayesactions4.1.2EmpiricalandhierarchicalBayesmethods4.1.3Bayesrulesandestimators4.1.4MarkovchainMollteCarlo4.2Invariance......4.2.1One-parameterlocationfamilies4.2.2One-parametersealefamilies4.2.3Generallocation-scalefamilies4.3MinimaxityandAdmissibility4.3.1Estimatorswithconstantrisks4.3.2Resultsinone-parameterexponentialfamilies4.3.3Simultaneousestimationandshrinkageestimators4.4TheMethodofMaximumLikelihood4.4.1ThelikelihoodfunctionandMLEs4.4.2MLEsingeneralizedlinearmodels4.4.3Quasi-likelihoodsandconditionallikelihoods4.5AsymptoticallyEfficientEstimation4.5.1Asymptoticoptimality4.5.2AsymptoticefficiencyofMLEsandRLEs4.5.3Otherasymptoticallyefficientestimators4.6ExercisesChapter5.EstimationinNonparametricModels5.1DistributionEstimators5.1.1EmpiricalC.d.f.sini.i.d.cases5.1.2Empiricallikelihoods5.1.3Densityestimation5.1.4Semi-parametricmethods5.2StatisticalFunctionals5.2.1Differentiabilityandasymptoticnormality5.2.2L-.M-.andR-estimatorsandrankstatistics5.3LinearFunctionsofOrderStatistics5.3.1Samplequantiles5.3.2R0bustnessandefficiency5.3.3L-estimatorsinlinearmodels5.4GeneralizedEstimatingEquations5.4.1TheGEEmethodanditsrelationshipwithothers5.4.2ConsistencyofGEEestimators5.4.3AsymptoticnormalityofGEEestimators5.5VarianceEstimation5.5.1Thesubstitution.method5.5.2Thejackknife5.5.3Thebootstrap5.6ExercisesChapter6.HypothesisTests6.1UMPTests6.1.1TheNeyman-Pearsonlemma6.1.2Monotonelikelihoodratio6.1.3UMPtestsfortwo-sidedhypotheses6.2UMPUnbiasedTests6.2.1Unbiasedness,similarity,andNeymanstructure6.2.2UMPUtestsinexponentialfamilies6.2.3UMPUtestsinnormalfamilies……Chapter7ConfidenceSetsReferencesListofNotationListofAbbreviationsIndexofDefinitions,MainResults,andExamplesAuthorIndexSubjectIndex
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