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书籍介绍
《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。
目录
- 1probabilitytheory
- 1.1settheory
- 1.2basicsofprobabilitytheory
- 1.2.1axiomaticfoundations
- 1.2.2thecalculusofprobabilities
- 1.2.3counting
- 1.2.4enumeratingoutcomes
- 1.3conditionalprobabilityandindependence
- 1.4randomvariables
- 1.5distributionfunctions
- 1.6densityandmassfunctions
- 1.7exercises
- 1.8miscellaneatransformationsandexpectations
- 2.1distributionsoffunctionsofarandomvariab]e
- 2.2expectedvalues
- 2.3momentsandmomentgeneratingfunctions
- 2.4differentiatingunderanintegralsign
- 2.5exercises
- 2.6miscellaneacommonfamiliesofdistributions
- 3.1introduction
- 3.2discretedistributions
- 3.3continuousdistributions
- 3.4exponentialfamilies
- 3.5locationandscalefamiliesinequalitiesandidentities
- 3.6.1probabilityinequalities
- 3.6.2identities
- 3.7exercises
- 3.8miscellanea
- 4multiplerandomvariables
- 4.1jointandmarginaldistributions
- 4.2conditionaldistributionsandindependence
- 4.3bivariatetransformations
- 4.4hierarchicalmodelsandmixturedistributions
- 4.5covarianceandcorrelation
- 4.6multivariatedistributions
- 4.7inequalities
- 4.7.1numericalinequalities
- 4.7.2functionalinequalities
- 4.8exercises
- 4.9miscellaneapropertiesofarandomsample
- 5.1basicconceptsofrandomsamples
- 5.2sumsofrandomvariablesfromarandomsample
- 5.3samplingfromthenormaldistribution
- 5.3.1propertiesofthesamplemeanandvariance
- 5.3.2thederiveddistributions:student'standsnedecor'sf
- 5.4orderstatistics
- 5.5convergenceconcepts
- 5.5.1convergenceinprobability
- 5.5.2almostsureconvergence
- 5.5.3convergenceindistribution
- 5.5.4thedeltamethod
- 5.6generatingarandomsample
- 5.6.1directmethods
- 5.6.2indirectmethods
- 5.6.3theaccept/rejectalgorithm
- 5.7exercises
- 5.8miscellaneaprinciplesofdatareduction
- 6.1introduction
- 6.2thesufficiencyprinciple
- 6.2.1sufficientstatistics
- 6.2.2minimalsufficientstatistics
- 6.2.3ancillarystatistics
- 6.2.4sufficient,ancillary,andcompletestatistics
- 6.3thelikelihoodprinciple
- 6.3.1thelikelihoodfunction
- 6.3.2theformallikelihoodprinciple
- 6.4theequivarianceprinciple
- 6.5exercises
- 6.6miscellanea
- pointestimation
- 7.1introduction
- 7.2methodsoffindingestimators
- 7.2.1methodofmoments
- 7.2.2maximumlikelihoodestimators
- 7.2.3bayesestimators
- 7.2.4theemalgorithm
- 7.3methodsofevaluatingestimators
- 7.3.1meansquarederror
- 7.3.2bestunbiasedestimators
- 7.3.3sufficiencyandunbiasedness
- 7.3.4lossfunctionoptimality
- 7.4exercises
- 7.5miscellaneahypothesistesting
- 8.1introduction
- 8.2methodsoffindingtests
- 8.2.1likelihoodratiotests
- 8.2.2bayesiantests
- 8.2.3union-intersectionandintersection-uniontests
- 8.3methodsofevaluatingtests
- 8.3.1errorprobabilitiesandthepowerfunction
- 8.3.2mostpowerfultests
- 8.3.3sizesof.union-intersectionandintersection-uniontests
- 8.3.4p-values
- 8.3.5lossfunctionoptimality
- 8.4exercises
- 8.5miscellanea
- intervalestimation
- 9.1introduction
- 9.2methodsoffindingintervalestimators
- 9.2.1invertingateststatistic
- 9.2.2pivotalquantities
- 9.2.3pivotingthecdf
- 9.2.4bayesianintervals
- 9.3methodsofevaluatingintervalestimators
- 9.3.1sizeandcoverageprobability
- 9.3.2test-relatedoptimality
- 9.3.3bayesianoptimality
- 9.3.4lossfunctionoptimality
- 9.4exercises
- 9.5miscellanea
- 10asymptoticevaluations
- 10.1pointestimation
- 10.1.1consistency
- 10.1.2efficiency
- 10.1.3calculationsandcomparisons
- 10.1.4bootstrapstandarderrors
- 10.2robustness
- 10.2.1themeanandthemedian
- 10.2.2m-estimators
- 10.3hypothesistesting
- 10.3.1asymptoticdistributionoflrts
- 10.3.2otherlarge-sampletests
- 10.4intervalestimation
- 10.4.1approximatemaximumlikelihoodintervals
- 10.4.2otherlarge-sampleintervals
- 10.5exercises
- 10.6miscellanea
- 11analysisofvarianceandregression
- 11.1introduction
- 11.2onewayanalysisofvariance
- 11.2.1modelanddistributionassumptions
- 11.2.2theclassicanovahypothesis
- 11.2:3inferencesregardinglinearcombinationsofmeans
- 11.2.4theanovaftest
- 11.2.5simultaneousestimationofcontrasts
- 11.2.6partitioningsumsofsquares
- 11.3simplelinearregression
- 11.3.1leastsquares:amathematicalsolution
- 11.3.2bestlinearunbiasedestimators:astatisticalsolution
- 11.3.3modelsanddistributionassumptions
- 11.3.4estimationandtestingwithnormalerrors
- 11.3.5estimationandpredictionataspecifiedx=x0
- 11.3.6simultaneousestimationandconfidencebands
- 11.4exercises
- 11.5miscellanea
- 12regressionmodels
- 12.1introduction
- 12.2regressionwitherrorsinvariables
- 12.2.1functionalandstructuralrelationships
- 12.2.2aleastsquaressolution
- 12.2.3maximumlikelihoodestimation
- 12.2.4confidencesets
- 12.3logisticregression
- 12.3.1themodel
- 12.3.2estimation
- 12.4robustregression
- 12.5exercises
- 12.6miscellanea
- appendix:computeralgebra
- tableofcommondistributions
- references
- authorindex
- subjectindex