统计理论.pdf

统计理论.pdf
 

书籍描述

编辑推荐
《统计理论(英文)》读者对象包括概率统计、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
作者:(美国)舍维什(Mark J.Schervish)

目录
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 DeFinetti's Representation Theorem
1.4.1 Understanding the Theorems
1.4.2 The Mathematical Statements
1.4.3 Some Examples
1.5 Proofs of DeFinetti's 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: Sufflcient 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
……
Chapter 3: Decision Theory
Chapter 4: Hypothesis Testing
Chapter 5: Estimation
Chapter 6: Equivariance
Chapter 8: Hierarchical Models
Chapter 9: Sequential Analysis
Appendix A: Measure and Integration Theory
Appendix B: Probability Theory

文摘
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内容简介
《统计理论(英文)》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。《统计理论(英文)》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。

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