统计推断

图书标准信息

• 作者 [美]卡塞拉（Casella G.） 著
• 出版社 机械工业出版社
• 出版时间 2002-10
• 版次 1
• ISBN 9787111109457
• 定价 39.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 660页
• 字数 824千字

【内容简介】

　　《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