《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。

《统计理论（英文*版）》
preface
chapter 1: probability models
1.1 background
1.1.1 general concepts
1.1.2 classical statistics
1.1.3 bayesian statistics
1.2 exchangeability
1.2.1 distributional symmetry
1.2.2 frequency and exchangeability
1.3 parametric models
1.3.1 prior， posterior， and predictive distributions
1.3.2 improper prior distributions
1.3.3 choosing probability distributions
1.4 definettis representation theorem《统计理论（英文*版）》
preface
chapter 1: probability models
1.1 background
1.1.1 general concepts
1.1.2 classical statistics
1.1.3 bayesian statistics
1.2 exchangeability
1.2.1 distributional symmetry
1.2.2 frequency and exchangeability
1.3 parametric models
1.3.1 prior， posterior， and predictive distributions
1.3.2 improper prior distributions
1.3.3 choosing probability distributions
1.4 definettis representation theorem
1.4.1 understanding the theorems
1.4.2 the mathematical statements
1.4.3 some examples
1.5 proofs of definettis theorem and related results*
1.5.1 strong law of large numbers
.1.5.2 the bernoulli case
1.5.3 the general finite case
1.5.4 the general infinite case
1.5.5 formal introduction to parametric models*
1.6 infinite-dimensional parameters*
1.6.1 dirichlet processes
1.6.2 tailfree processes+
1.7 problems
chapter 2: sufficient statistics
2.1 definitions
2.1.1 notational overview
2.1.2 sufficiency
2.1.3 minimal and complete sufficiency
2.1.4 ancillarity
2.2 exponential families of distributions
2.2.1 basic properties
2.2.2 smoothness properties
2.2.3 a characterization theorem*
2.3 information
2.3.1 fisher information
2.3.2 kullback-leibler information
2.3.3 conditional information*
2.3.4 jeffreys prior*
2.4 extremal families
2.4.1 the main results
2.4.2 examples
2.4.3 proofs+
2.5 problems
chapter 3: decision theory
3.1decision problems
3.1.1 framework
3.1.2 elements of bayesian decision theory
3.1.3 elements of classical decision theory
3.1.4 summary
3.2 classical decision theory
3.2.1 the role of sufficient statistics
3.2.2 admissibility
3.2.3 james-stein estimators
3.2.4 minimax rules
3.2.5 complete classes
3.3 axiomatic derivation of decision theory
3.3.1 definitions and axioms
3.3.2 examples
3.3.3 the main theorems
3.3.4 relation to decision theory
3.3.5 proofs of the main theorems
3.3.6 state-dependent utility*
3.4 problems:
chapter 4: hypothesis testing
4.1 introduction
4.1.1 a special kind of decision problem
4.1.2 pure significance tests
4.2 bayesian solutions
4.2.1 testing in general
4.2.2 bayes factors
4.3 most powerful tests
4.3.1 simple hypotheses and alternatives
4.3.2 simple hypotheses， composite alternatives
4.3.3 one-sided tests
4.3.4 two-sided hypotheses
4.4 unbiased tests
4.4. i general results
4.4.2 interval hypotheses
4.4.3 point hypotheses
4.5 nuisance parameters
4.5.1 neyman structure
4.5.2 tests about natural parameters
4.5.3 linear combinations of natural parameters
4.5.4 other two-sided cases
4.5.5 likelihood ratio tests
4.5.6 the standard f-test as a bayes rule*.
4.6 p-values
4.6.1 definitions and examples
4.6.2 p-values and bayes factors
4.7 problems
chapter 5: estimation
5.1 point estimation
5.1.1 minimum variance unbiased estimation
5.1.2 lower bounds on the variance of unbiased estimators
5.1.3 maximum likelihood estimation
5.1.4 bayesian estimation
5.1.5 robust estimation*
5.2 set estimation
5.2.1 confidence sets
5.2.2 prediction sets*
5.2.3 tolerance sets*
5.2.4 bayesian set estimation
5.2.5 decision theoretic set es

暂无