數理統計(第2版)（簡體書）

《數理統計(第2版)(英文版)》內容簡介：Probability Theory、Probability Spaces and Random Elements、σ－fields and measures、Measurable functions and distributions、Integration and Differentiation、Integration、Radon.Nikodym derivative、Distributions and Their Characteristics、Distributions and probability densities、Moments and moment inequalities、Moment generating and characteristic functions、onditional Expectations、Conditional expectations、Independence、Conditional distributions、Markov chains and martingales、Asymptotic Theory、Convergence modes and stochastic orders等等。本書是一部著名的研究生教材，內容簡明，結構嚴謹，論述清晰，書中不僅論述了統計理論的基本概念，同時也包括現代統計理論，如馬爾科夫鏈、蒙特卡羅方法、半參數模型與方法、統計、廣義估計方程和自助法等。各章有上百例練習題。另外，與本書配套的Mathematical Statistical Statistics: Exercises and Solutions近期也將由世圖影印出版，敬請關注。目次：概率論；統計學基礎；無偏估計；參數模型中的估計；非參數模型中的估計；假想測試；置信集。
讀者對象：數理統計專業的研究生。

Preface to the First Edition
Preface to the Second Edition
Chapter 1. Probability Theory
　1.1 Probability Spaces and Random Elements
1.1.1 a-fields and measures
1.1.2 Measurable functions and distributions
　1.2 Integration and Differentiation
1.2.1 Integration
1.2.2 Radon-Nikodym derivative
　1.3 Distributions and Their Characteristics
1.3.1 Distributions and probability densities
1.3.2 Moments and moment inequalities
1.3.3 Moment generating and characteristic functions
　1.4 Conditional Expectations
1.4.1 Conditional expectations
1.4.2 Independence
1.4.3 Conditional distributions
1.4.4 Markov chains and martingales
1.5 Asymptotic Theory
1.5.1 Convergence modes and stochastic orders
1.5.2 Weak convergence
1.5.3 Convergence of transformations
1.5.4 The law of large numbers
1.5.5 The central limit theorem
1.5.6 Edgeworth and Cornish-Fisher expansions
　1.6 Exercises
Chapter 2. Fundamentals of Statistics
　2.1 Populations, Samples, and Models
2.1.1 Populations and samples
2.1.2 Parametric and nonparametric models
2.1.3 Exponential and location-scale families
　2.2 Statistics, Sufficiency, and Completeness
2.2.1 Statistics and their distributions
2.2.2 Sufficiency and minimal sufficiency
2.2.3 Complete statistics
　2.3 Statistical Decision Theory
2.3.1 Decision rules, loss functions, and risks
2.3.2 Admissibility and optimMity
　2.4 Statistical Inference
2.4.1 Point estimators
2.4.2 Hypothesis tests
2.4.3 Confidence sets
　2.5 Asymptotic Criteria and Inference
2.5.1 Consistency
2.5.2 Asymptotic bias, variance, and mse
2.5.3 Asymptotic inference
　2.6 Exercises
Chapter 3. Unbiased Estimation
3.1 The UMVUE
3.1.1 Sufficient and complete statistics
3.1.2 A necessary andsufficient condition
3.1.3 Information inequality
3.1.4 Asymptotic properties of UMVUEs
3.2 U-Statistics
3.2.1 Some examples
3.2.2 Variances of U-statistics
3.2.3 The projection method
　……
Chapter 4. Estimation in Parametric Models
Chapter 5. Estimation in Nonparametric Models
Chapter 6. Hypothesis Tests
Chapter 7. Confidence Sets
References
List of Notation
List of Abbreviations
Index of Definitions, Main Results, and Examples
Author Index
Subject Index