统计理论-(影印版)
节选
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舍维什编著的这本《统计理论》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。本书目次如下: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。
本书读者对象: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。
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本书特色
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舍维什编著的这本《统计理论》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。本书目次如下: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。
本书读者对象: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。
]
内容简介
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《统计理论》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。
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。
]
目录
《统计理论(英文影印版)》prefacechapter 1: probability models1.1 background1.1.1 general concepts1.1.2 classical statistics1.1.3 bayesian statistics1.2 exchangeability1.2.1 distributional symmetry1.2.2 frequency and exchangeability1.3 parametric models1.3.1 prior, posterior, and predictive distributions1.3.2 improper prior distributions1.3.3 choosing probability distributions1.4 definetti’s representation theorem 《统计理论(英文影印版)》prefacechapter 1: probability models1.1 background1.1.1 general concepts1.1.2 classical statistics1.1.3 bayesian statistics1.2 exchangeability1.2.1 distributional symmetry1.2.2 frequency and exchangeability1.3 parametric models1.3.1 prior, posterior, and predictive distributions1.3.2 improper prior distributions1.3.3 choosing probability distributions1.4 definetti’s representation theorem1.4.1 understanding the theorems1.4.2 the mathematical statements1.4.3 some examples1.5 proofs of definetti’s theorem and related results*1.5.1 strong law of large numbers.1.5.2 the bernoulli case1.5.3 the general finite case’1.5.4 the general infinite case1.5.5 formal introduction to parametric models*1.6 infinite-dimensional parameters*1.6.1 dirichlet processes1.6.2 tailfree processes+1.7 problemschapter 2: sufficient statistics2.1 definitions2.1.1 notational overview2.1.2 sufficiency2.1.3 minimal and complete sufficiency2.1.4 ancillarity2.2 exponential families of distributions2.2.1 basic properties2.2.2 smoothness properties2.2.3 a characterization theorem*2.3 information2.3.1 fisher information2.3.2 kullback-leibler information2.3.3 conditional information*2.3.4 jeffreys’ prior*2.4 extremal families’2.4.1 the main results2.4.2 examples2.4.3 proofs+2.5 problemschapter 3: decision theory3.1decision problems3.1.1 framework3.1.2 elements of bayesian decision theory3.1.3 elements of classical decision theory3.1.4 summary3.2 classical decision theory3.2.1 the role of sufficient statistics3.2.2 admissibility3.2.3 james-stein estimators3.2.4 minimax rules3.2.5 complete classes3.3 axiomatic derivation of decision theory’3.3.1 definitions and axioms3.3.2 examples3.3.3 the main theorems3.3.4 relation to decision theory3.3.5 proofs of the main theorems’3.3.6 state-dependent utility*3.4 problems:chapter 4: hypothesis testing4.1 introduction4.1.1 a special kind of decision problem4.1.2 pure significance tests4.2 bayesian solutions4.2.1 testing in general4.2.2 bayes factors4.3 most powerful tests4.3.1 simple hypotheses and alternatives4.3.2 simple hypotheses, composite alternatives4.3.3 one-sided tests4.3.4 two-sided hypotheses4.4 unbiased tests4.4. i general results4.4.2 interval hypotheses4.4.3 point hypotheses4.5 nuisance parameters4.5.1 neyman structure4.5.2 tests about natural parameters4.5.3 linear combinations of natural parameters4.5.4 other two-sided cases’4.5.5 likelihood ratio tests4.5.6 the standard f-test as a bayes rule*.4.6 p-values4.6.1 definitions and examples4.6.2 p-values and bayes factors4.7 problemschapter 5: estimation5.1 point estimation5.1.1 minimum variance unbiased estimation5.1.2 lower bounds on the variance of unbiased estimators5.1.3 maximum likelihood estimation5.1.4 bayesian estimation5.1.5 robust estimation*5.2 set estimation5.2.1 confidence sets5.2.2 prediction sets*5.2.3 tolerance sets*5.2.4 bayesian set estimation5.2.5 decision theoretic set estimation’5.3 the bootstrap*5.3.1 the general concept5.3.2 standard deviations and bias5.3.3 bootstrap confidence intervals5.4 problemschapter 6: equivariance6.1 common examples6.1.1 location problems6.1.2 scale problems’6.2 equivariant decision theory6.2.1 groups of transformations6.2.2 equivariance and changes of units6.2.3 minimum risk equivariant decisions6.3 testing and confidence intervals’6.3.1 p-values in invariant problems6.3.2 equivariant confidence sets6.3.3 invariant tests*6.4 problemschapter 7: large sample theory7.1 convergence concepts7.1.1 deterministic convergence7.1.2 stochastic convergence7.1.3 the delta method7.2 sample quantiles7.2.1 a single quantile7.2.2 several quantiles7.2.3 linear combinations of quantiles’7.3 large sample estimation7.3.1 some principles of large sample estimation7.3.2 maximum likelihood estimators7.3.3 mles in exponential families7.3.4 examples of inconsistent mles7.3.5 asymptotic normality of mles7.3.6 asymptotic properties of m-estimators’7.4 large sample properties of posterior distributions7.4.1 consistency of posterior distributions+7.4.2 asymptotic normality of posterior distributions7.4.3 laplace approximations to posterior distributions*7.4.4 asymptotic agreement of predictive distributions+7.5 large sample tests7.5.1 likelihood ratio tests7.5.2 chi-squared goodness of fit tests7.6 problemschapter 8: hierarchical models8.1 introduction8.1.1 general hierarchical models8.1.2 partial exchangeability’8.1.3 examples of the representation theorem’8.2 normal linear models8.2.1 one-way anova8.2.2 two-way mixed model anova’8.2.3 hypothesis testing8.3 nonnormal models’8.3.1 poisson process data8.3.2 bernoulli process data8.4 empirical bayes analysis*8.4.1 nayve empirical bayes8.4.2 adjusted empirical bayes8.4.3 unequal variance case8.5 successive substitution sampling8.5.1 the general algorithm8.5.2 normal hierarchical models8.5.3 nonnormal models8.6 mixtures of models8.6.1 general mixture models8.6.2 outliers8.6.3 bayesian robustness8.7 problemschapter 9: sequential analysis9.1 sequential decision problems9.2 the sequential probability ratio test9.3 interval estimation*9.4 the relevance of stopping rules9.5 problemsappendix a: measure and integration theorya.1 overviewa.1.1 definitionsa.1.2 measurable functionsa.1.3 integrationa.1.4 absolute continuitya.2 measuresa.3 measurable functionsa.4 integrationa.5 product spacesa.6 absolute continuitya.7 problemsappendix b: probability theoryb.1 overviewb.i.1 mathematical probabilityb.l.2 conditioningb.1.3 limit theoremsb.2 mathematical probabilityb.2.1 random quantities and distributionsb.2.2 some useful inequalitiesb.3 conditioningb.3.1 conditional expectationsb.3.2 borel spaces’b.3.3 conditional densitiesb.3.4 conditional independenceb.3.5 the law of total probabilityb.4 limit theoremsb.4.1 convergence in distribution and in probabilityb.4.2 characteristic functionsb.5 stochastic processesb.5.1 introductionb.5.2 martingales+b.5.3 markov chains*b.5.4 general stochastic processesb.6 subjective probabilityb.7 simulation*b.8 problemsappendix c: mathematical theorems not proven herec.1 real analysisc.2 complex analysisc.3 functional analysisappendix d: summary of distributionsd.1 univariate continuous distributionsd.2 univariate discrete distributionsd.3 multivariate distributionsreferencesnotation and abbreviation indexname indexsubject index
封面
书名:统计理论-(影印版)
作者:舍维什
页数:702
定价:¥109.0
出版社:世界图书出版公司
出版日期:2014-01-01
ISBN:9787510068119
PDF电子书大小:99MB 高清扫描完整版