![主编推荐]()
After a brief review of elementary statistical theory， the coverage of thesubject matter begins with a detailed treatment of parametric statisticalmodels as motivated by DeFinetti's representation theorem for exchangeablerandom variables （Chapter l）. In addition， Dirichlet processes and othertailfree processes are presented as examples of infinite-dimensional param-etenull
![内容简介]()
《数学与金融经典教材：统计理论（影印版）》是一部经典的讲述统计理论的研究生教程，综合性强，内容涵盖：估计；检验；大样本理论，这些都是研究生要进入博士或者更高层次必须学习的预备知识。为了让读者具备更加强硬的数学背景和更广阔的理论知识，书中不仅给出了经典方法，也给出了贝叶斯推理知识。目次：概率模型；充分统计量；决策理论；假设检验；估计；等价；大样本理论；分层模型；序列分析；附录：测度与积分理论；概率论；数学定理；分布概述。
《数学与金融经典教材：统计理论（影印版）》读者对象：概率统计、数学专业以及相关专业的高年级本科生、研究生和相关的科研人员。
![作者简介]()
无
![精彩内容]()
无
![目录]()
《统计理论（英文影印版）》
preface
chapter1:probabilitymodels
1.1background
1.1.1generalconcepts
1.1.2classicalstatistics
1.1.3bayesianstatistics
1.2exchangeability
1.2.1distributionalsymmetry
1.2.2frequencyandexchangeability
1.3parametricmodels
1.3.1prior,posterior,andpredictivedistributions
1.3.2improperpriordistributions
1.3.3choosingprobabilitydistributions
1.4definetti'srepresentationtheorem
1.4.1understandingthetheorems
1.4.2themathematicalstatements
1.4.3someexamples
1.5proofsofdefinetti'stheoremandrelatedresults*
1.5.1stronglawoflargenumbers
.1.5.2thebernoullicase
1.5.3thegeneralfinitecase'
1.5.4thegeneralinfinitecase
1.5.5formalintroductiontoparametricmodels*
1.6infinite-dimensionalparameters*
1.6.1dirichletprocesses
1.6.2tailfreeprocesses+
1.7problems
chapter2:sufficientstatistics
2.1definitions
2.1.1notationaloverview
2.1.2sufficiency
2.1.3minimalandcompletesufficiency
2.1.4ancillarity
2.2exponentialfamiliesofdistributions
2.2.1basicproperties
2.2.2smoothnessproperties
2.2.3acharacterizationtheorem*
2.3information
2.3.1fisherinformation
2.3.2kullback-leiblerinformation
2.3.3conditionalinformation*
2.3.4jeffreys'prior*
2.4extremalfamilies'
2.4.1themainresults
2.4.2examples
2.4.3proofs+
2.5problems
chapter3:decisiontheory
3.1decisionproblems
3.1.1framework
3.1.2elementsofbayesiandecisiontheory
3.1.3elementsofclassicaldecisiontheory
3.1.4summary
3.2classicaldecisiontheory
3.2.1theroleofsufficientstatistics
3.2.2admissibility
3.2.3james-steinestimators
3.2.4minimaxrules
3.2.5completeclasses
3.3axiomaticderivationofdecisiontheory'
3.3.1definitionsandaxioms
3.3.2examples
3.3.3themaintheorems
3.3.4relationtodecisiontheory
3.3.5proofsofthemaintheorems'
3.3.6state-dependentutility*
3.4problems:
chapter4:hypothesistesting
4.1introduction
4.1.1aspecialkindofdecisionproblem
4.1.2puresignificancetests
4.2bayesiansolutions
4.2.1testingingeneral
4.2.2bayesfactors
4.3mostpowerfultests
4.3.1simplehypothesesandalternatives
4.3.2simplehypotheses,compositealternatives
4.3.3one-sidedtests
4.3.4two-sidedhypotheses
4.4unbiasedtests
4.4.igeneralresults
4.4.2intervalhypotheses
4.4.3pointhypotheses
4.5nuisanceparameters
4.5.1neymanstructure
4.5.2testsaboutnaturalparameters
4.5.3linearcombinationsofnaturalparameters
4.5.4othertwo-sidedcases'
4.5.5likelihoodratiotests
4.5.6thestandardf-testasabayesrule*.
4.6p-values
4.6.1definitionsandexamples
4.6.2p-valuesandbayesfactors
4.7problems
chapter5:estimation
5.1pointestimation
5.1.1minimumvarianceunbiasedestimation
5.1.2lowerboundsonthevarianceofunbiasedestimators
5.1.3maximumlikelihoodestimation
5.1.4bayesianestimation
5.1.5robustestimation*
5.2setestimation
5.2.1confidencesets
5.2.2predictionsets*
5.2.3tolerancesets*
5.2.4bayesiansetestimation
5.2.5decisiontheoreticsetestimation'
5.3thebootstrap*
5.3.1thegeneralconcept
5.3.2standarddeviationsandbias
5.3.3bootstrapconfidenceintervals
5.4problems
chapter6:equivariance
6.1commonexamples
6.1.1locationproblems
6.1.2scaleproblems'
6.2equivariantdecisiontheory
6.2.1groupsoftransformations
6.2.2equivarianceandchangesofunits
6.2.3minimumriskequivariantdecisions
6.3testingandconfidenceintervals'
6.3.1p-valuesininvariantproblems
6.3.2equivariantconfidencesets
6.3.3invarianttests*
6.4problems
chapter7:largesampletheory
7.1convergenceconcepts
7.1.1deterministicconvergence
7.1.2stochasticconvergence
7.1.3thedeltamethod
7.2samplequantiles
7.2.1asinglequantile
7.2.2severalquantiles
7.2.3linearcombinationsofquantiles'
7.3largesampleestimation
7.3.1someprinciplesoflargesampleestimation
7.3.2maximumlikelihoodestimators
7.3.3mlesinexponentialfamilies
7.3.4examplesofinconsistentmles
7.3.5asymptoticnormalityofmles
7.3.6asymptoticpropertiesofm-estimators'
7.4largesamplepropertiesofposteriordistributions
7.4.1consistencyofposteriordistributions+
7.4.2asymptoticnormalityofposteriordistributions
7.4.3laplaceapproximationstoposteriordistributions*
7.4.4asymptoticagreementofpredictivedistributions+
7.5largesampletests
7.5.1likelihoodratiotests
7.5.2chi-squaredgoodnessoffittests
7.6problems
chapter8:hierarchicalmodels
8.1introduction
8.1.1generalhierarchicalmodels
8.1.2partialexchangeability'
8.1.3examplesoftherepresentationtheorem'
8.2normallinearmodels
8.2.1one-wayanova
8.2.2two-waymixedmodelanova'
8.2.3hypothesistesting
8.3nonnormalmodels'
8.3.1poissonprocessdata
8.3.2bernoulliprocessdata
8.4empiricalbayesanalysis*
8.4.1nayveempiricalbayes
8.4.2adjustedempiricalbayes
8.4.3unequalvariancecase
8.5successivesubstitutionsampling
8.5.1thegeneralalgorithm
8.5.2normalhierarchicalmodels
8.5.3nonnormalmodels
8.6mixturesofmodels
8.6.1generalmixturemodels
8.6.2outliers
8.6.3bayesianrobustness
8.7problems
chapter9:sequentialanalysis
9.1sequentialdecisionproblems
9.2thesequentialprobabilityratiotest
9.3intervalestimation*
9.4therelevanceofstoppingrules
9.5problems
appendixa:measureandintegrationtheory
a.1overview
a.1.1definitions
a.1.2measurablefunctions
a.1.3integration
a.1.4absolutecontinuity
a.2measures
a.3measurablefunctions
a.4integration
a.5productspaces
a.6absolutecontinuity
a.7problems
appendixb:probabilitytheory
b.1overview
b.i.1mathematicalprobability
b.l.2conditioning
b.1.3limittheorems
b.2mathematicalprobability
b.2.1randomquantitiesanddistributions
b.2.2someusefulinequalities
b.3conditioning
b.3.1conditionalexpectations
b.3.2borelspaces'
b.3.3conditionaldensities
b.3.4conditionalindependence
b.3.5thelawoftotalprobability
b.4limittheorems
b.4.1convergenceindistributionandinprobability
b.4.2characteristicfunctions
b.5stochasticprocesses
b.5.1introduction
b.5.2martingales+
b.5.3markovchains*
b.5.4generalstochasticprocesses
b.6subjectiveprobability
b.7simulation*
b.8problems
appendixc:mathematicaltheoremsnotprovenhere
c.1realanalysis
c.2complexanalysis
c.3functionalanalysis
appendixd:summaryofdistributions
d.1univariatecontinuousdistributions
d.2univariatediscretedistributions
d.3multivariatedistributions
references
notationandabbreviationindex
nameindex
subjectindex
