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[美] 卡塞拉 (Casella G.) 著 / 机械工业出版社 / 2002-10 / 平装
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统计推断
《统计推断》(英文版)(原书第2版)从概率论的基础开始,通过例子与习题的旁征博引,引进了大量近代统计处理的新技术和一些国内同类教材中不能见而广为使用的分布。其内容包括工科概率论入门、经典统计和现代统计的基础,又加进了不少近代统计中数据处理的实用方法和思想,例如:Bootstrap再抽样法、刀切(Jackknife)估计、EM算法、Logistic回归、稳健(Robust)回归、Markov链、MonteCarlo方法等。它的统计内容与国内流行的教材相比,理论较深,模型较多,案例的涉及面要广,理论的应用面要丰富,统计思想的阐述与算法更为具体。
1probabilitytheory1.1settheory1.2basicsofprobabilitytheory1.2.1axiomaticfoundations1.2.2thecalculusofprobabilities1.2.3counting1.2.4enumeratingoutcomes1.3conditionalprobabilityandindependence1.4randomvariables1.5distributionfunctions1.6densityandmassfunctions1.7exercises1.8miscellaneatransformationsandexpectations2.1distributionsoffunctionsofarandomvariab]e2.2expectedvalues2.3momentsandmomentgeneratingfunctions2.4differentiatingunderanintegralsign2.5exercises2.6miscellaneacommonfamiliesofdistributions3.1introduction3.2discretedistributions3.3continuousdistributions3.4exponentialfamilies3.5locationandscalefamiliesinequalitiesandidentities3.6.1probabilityinequalities3.6.2identities3.7exercises3.8miscellanea4multiplerandomvariables4.1jointandmarginaldistributions4.2conditionaldistributionsandindependence4.3bivariatetransformations4.4hierarchicalmodelsandmixturedistributions4.5covarianceandcorrelation4.6multivariatedistributions4.7inequalities4.7.1numericalinequalities4.7.2functionalinequalities4.8exercises4.9miscellaneapropertiesofarandomsample5.1basicconceptsofrandomsamples5.2sumsofrandomvariablesfromarandomsample5.3samplingfromthenormaldistribution5.3.1propertiesofthesamplemeanandvariance5.3.2thederiveddistributions:student'standsnedecor'sf5.4orderstatistics5.5convergenceconcepts5.5.1convergenceinprobability5.5.2almostsureconvergence5.5.3convergenceindistribution5.5.4thedeltamethod5.6generatingarandomsample5.6.1directmethods5.6.2indirectmethods5.6.3theaccept/rejectalgorithm5.7exercises5.8miscellaneaprinciplesofdatareduction6.1introduction6.2thesufficiencyprinciple6.2.1sufficientstatistics6.2.2minimalsufficientstatistics6.2.3ancillarystatistics6.2.4sufficient,ancillary,andcompletestatistics6.3thelikelihoodprinciple6.3.1thelikelihoodfunction6.3.2theformallikelihoodprinciple6.4theequivarianceprinciple6.5exercises6.6miscellaneapointestimation7.1introduction7.2methodsoffindingestimators7.2.1methodofmoments7.2.2maximumlikelihoodestimators7.2.3bayesestimators7.2.4theemalgorithm7.3methodsofevaluatingestimators7.3.1meansquarederror7.3.2bestunbiasedestimators7.3.3sufficiencyandunbiasedness7.3.4lossfunctionoptimality7.4exercises7.5miscellaneahypothesistesting8.1introduction8.2methodsoffindingtests8.2.1likelihoodratiotests8.2.2bayesiantests8.2.3union-intersectionandintersection-uniontests8.3methodsofevaluatingtests8.3.1errorprobabilitiesandthepowerfunction8.3.2mostpowerfultests8.3.3sizesof.union-intersectionandintersection-uniontests8.3.4p-values8.3.5lossfunctionoptimality8.4exercises8.5miscellaneaintervalestimation9.1introduction9.2methodsoffindingintervalestimators9.2.1invertingateststatistic9.2.2pivotalquantities9.2.3pivotingthecdf9.2.4bayesianintervals9.3methodsofevaluatingintervalestimators9.3.1sizeandcoverageprobability9.3.2test-relatedoptimality9.3.3bayesianoptimality9.3.4lossfunctionoptimality9.4exercises9.5miscellanea10asymptoticevaluations10.1pointestimation10.1.1consistency10.1.2efficiency10.1.3calculationsandcomparisons10.1.4bootstrapstandarderrors10.2robustness10.2.1themeanandthemedian10.2.2m-estimators10.3hypothesistesting10.3.1asymptoticdistributionoflrts10.3.2otherlarge-sampletests10.4intervalestimation10.4.1approximatemaximumlikelihoodintervals10.4.2otherlarge-sampleintervals10.5exercises10.6miscellanea11analysisofvarianceandregression11.1introduction11.2onewayanalysisofvariance11.2.1modelanddistributionassumptions11.2.2theclassicanovahypothesis11.2:3inferencesregardinglinearcombinationsofmeans11.2.4theanovaftest11.2.5simultaneousestimationofcontrasts11.2.6partitioningsumsofsquares11.3simplelinearregression11.3.1leastsquares:amathematicalsolution11.3.2bestlinearunbiasedestimators:astatisticalsolution11.3.3modelsanddistributionassumptions11.3.4estimationandtestingwithnormalerrors11.3.5estimationandpredictionataspecifiedx=x011.3.6simultaneousestimationandconfidencebands11.4exercises11.5miscellanea12regressionmodels12.1introduction12.2regressionwitherrorsinvariables12.2.1functionalandstructuralrelationships12.2.2aleastsquaressolution12.2.3maximumlikelihoodestimation12.2.4confidencesets12.3logisticregression12.3.1themodel12.3.2estimation12.4robustregression12.5exercises12.6miscellaneaappendix:computeralgebratableofcommondistributionsreferencesauthorindexsubjectindex
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