Mathematical Statistics

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1、JunShaoMathematicalStatisticsSecondEditionContentsPrefacetotheFirstEditionviiPrefacetotheSecondEditionixChapter1.ProbabilityTheory11.1ProbabilitySpacesandRandomElements...........11.1.1σ-fieldsandmeasures..................11.1.2Measurablefunctionsanddistributions........61.2IntegrationandDifferen

2、tiation.................101.2.1Integration........................101.2.2Radon-Nikodymderivative...............151.3DistributionsandTheirCharacteristics............171.3.1Distributionsandprobabilitydensities........171.3.2Momentsandmomentinequalities...........281.3.3Momentgeneratingandcharacte

3、risticfunctions...321.4ConditionalExpectations....................371.4.1Conditionalexpectations................371.4.2Independence......................411.4.3Conditionaldistributions................431.4.4Markovchainsandmartingales.............451.5AsymptoticTheory.......................491.5

4、.1Convergencemodesandstochasticorders.......501.5.2Weakconvergence....................561.5.3Convergenceoftransformations............591.5.4Thelawoflargenumbers................621.5.5Thecentrallimittheorem................67xixiiContents1.5.6EdgeworthandCornish-Fisherexpansions......701.6Exercis

5、es.............................74Chapter2.FundamentalsofStatistics912.1Populations,Samples,andModels...............912.1.1Populationsandsamples................912.1.2Parametricandnonparametricmodels.........942.1.3Exponentialandlocation-scalefamilies........962.2Statistics,Sufficiency,andComplete

6、ness............1002.2.1Statisticsandtheirdistributions............1002.2.2Sufficiencyandminimalsufficiency..........1032.2.3Completestatistics...................1092.3StatisticalDecisionTheory...................1132.3.1Decisionrules,lossfunctions,andrisks........1132.3.2Admissibilityandoptimality.

7、.............1162.4StatisticalInference.......................1222.4.1Pointestimators.....................1222.4.2Hypothesistests.....................1252.4.3Confidencesets.....................1292.5AsymptoticCriteriaandInference..