数理统计第2版

图书标准信息

• 作者 [美]邵 著
• 出版社 世界图书出版公司
• 出版时间 2009-10
• 版次 1
• ISBN 9787510005343
• 定价 65.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 591页
• 正文语种 英语
• 原版书名 Mathematical Statistics(Second Edition)

【内容简介】

　　ProbabilityTheory、ProbabilitySpacesandRandomElements、σ－fieldsandmeasures、Measurablefunctionsanddistributions、IntegrationandDifferentiation、Integration、Radon.Nikodymderivative、DistributionsandTheirCharacteristics、Distributionsandprobabilitydensities、Momentsandmomentinequalities、Momentgeneratingandcharacteristicfunctions、onditionalExpectations、Conditionalexpectations、Independence、Conditionaldistributions、Markovchainsandmartingales、AsymptoticTheory、Convergencemodesandstochasticorders等等。

【目录】

PrefacetotheFirstEdition
PrefacetotheSecondEdition
Chapter1.ProbabilityTheory
1.1ProbabilitySpacesandRandomElements
1.1.1σ－fieldsandmeasures
1.1.2Measurablefunctionsanddistributions
1.2IntegrationandDifferentiation
1.2.1Integration
1.2.2Radon.Nikodymderivative
1.3DistributionsandTheirCharacteristics
1.3.1Distributionsandprobabilitydensities
1.3.2Momentsandmomentinequalities
1.3.3Momentgeneratingandcharacteristicfunctions
1.4ConditionalExpectations
1.4.1Conditionalexpectations
1.4.2Independence
1.4.3Conditionaldistributions
1.4.4Markovchainsandmartingales
1.5AsymptoticTheory
1.5.1Convergencemodesandstochasticorders
1.5.2Weakconvergence
1.5.3Convergenceoftransformations
1.5.4Thelawoflargenumbers
1.5.5Thecentrallimittheorem
1.5.6EdgeworthandCornish-Fisherexpansions
1.6Exercises

Chapter2.FundamentalsofStatistics
2.1Populations，Samples，andModels
2.1.1Populationsandsamples
2.1.2Parametricandnonparametricmodels
2.1.3Exponentialandlocation.scalefamilies
2.2Statistics.Sufficiency，andCompleteness
2.2.1Statisticsandtheirdistributions
2.2.2Sufficiencyandminimalsufficiency
2.2.3Completestatistics
2.3StatisticalDecisionTheory
2.3.1Decisionrules，lOSSfunctions，andrisks
2.3.2Admissibilityandoptimality
2.4StatisticalInference
2.4.1P0il）testimators
2.4.2Hypothesistests
2.4.3Confidencesets
2.5AsymptoticCriteriaandInference
2.5.1Consistency
2.5.2Asymptoticbias，variance，andmse
2.5.3Asymptoticinference
2.6Exercises

Chapter3.UnbiasedEstimation
3.1TheUMVUE
3.1.1Sufficientandcompletestatistics
3.1.2Anecessaryand.sufficientcondition
3.1.3Informationinequality
3.1.4AsymptoticpropertiesofUMVUEs
3.2U-Statistics
3.2.1Someexamples
3.2.2VariancesofU-statistics
3.2.3Theprojectionmethod
3.3TheLSEinLinearModels
3.3.1TheLSEandestimability
3.3.2TheUMVUEandBLUE
3.3.3R0bustnessofLSEs
3.3.4AsymptoticpropertiesofLSEs
3.4UnbiasedEstimatorsinSurveyProblems
3.4.1UMVUEsofpopulationtotals
3.4.2Horvitz-Thompsonestimators
3.5AsymptoticallyUnbiasedEstimators
3.5.1Functionsofunbiasedestimators
3.5.2Themethodofmoments
3.5.3V-statistics
3.5.4TheweightedLSE
3.6Exercises

Chapter4.EstimationinParametricModels
4.1BayesDecisionsandEstimators
4.1.1Bayesactions
4.1.2EmpiricalandhierarchicalBayesmethods
4.1.3Bayesrulesandestimators
4.1.4MarkovchainMollteCarlo
4.2Invariance......
4.2.1One-parameterlocationfamilies
4.2.2One-parametersealefamilies
4.2.3Generallocation-scalefamilies
4.3MinimaxityandAdmissibility
4.3.1Estimatorswithconstantrisks
4.3.2Resultsinone-parameterexponentialfamilies
4.3.3Simultaneousestimationandshrinkageestimators
4.4TheMethodofMaximumLikelihood
4.4.1ThelikelihoodfunctionandMLEs
4.4.2MLEsingeneralizedlinearmodels
4.4.3Quasi-likelihoodsandconditionallikelihoods
4.5AsymptoticallyEfficientEstimation
4.5.1Asymptoticoptimality
4.5.2AsymptoticefficiencyofMLEsandRLEs
4.5.3Otherasymptoticallyefficientestimators
4.6Exercises

Chapter5.EstimationinNonparametricModels
5.1DistributionEstimators
5.1.1EmpiricalC.d.f.sini.i.d.cases
5.1.2Empiricallikelihoods
5.1.3Densityestimation
5.1.4Semi-parametricmethods
5.2StatisticalFunctionals
5.2.1Differentiabilityandasymptoticnormality
5.2.2L-.M-.andR-estimatorsandrankstatistics
5.3LinearFunctionsofOrderStatistics
5.3.1Samplequantiles
5.3.2R0bustnessandefficiency
5.3.3L-estimatorsinlinearmodels
5.4GeneralizedEstimatingEquations
5.4.1TheGEEmethodanditsrelationshipwithothers
5.4.2ConsistencyofGEEestimators
5.4.3AsymptoticnormalityofGEEestimators
5.5VarianceEstimation
5.5.1Thesubstitution.method
5.5.2Thejackknife
5.5.3Thebootstrap
5.6Exercises

Chapter6.HypothesisTests
6.1UMPTests
6.1.1TheNeyman-Pearsonlemma
6.1.2Monotonelikelihoodratio
6.1.3UMPtestsfortwo-sidedhypotheses
6.2UMPUnbiasedTests
6.2.1Unbiasedness，similarity，andNeymanstructure
6.2.2UMPUtestsinexponentialfamilies
6.2.3UMPUtestsinnormalfamilies
……
Chapter7ConfidenceSets
References
ListofNotation
ListofAbbreviations
IndexofDefinitions，MainResults，andExamples
AuthorIndex
SubjectIndex