数理统计

数理统计

张进, 著

出版社:科学出版社

年代:2013

定价:37.0

书籍简介:

本书是作者根据多年在国内外高校从事教学和科研的经验,专门为英语为非母语的读者精细撰写的英文专著,系统而简明地介绍了《数理统计》的基本方法和理论,并配有适量精选的习题供读者练习。全书共分6章,内容包括:统计数据与模型、参数估计方法、优良性准则、假设检验与置信区域、渐近性理论及多参数渐近性理论。

书籍目录:

1 Statistical Models and Principles

1.1 Statistical Models

1.1.1 Data and Models

1.1.2 Parameters and Statistics

1.2 Bayesian Models

1.3 The Framework of Decision Theory

1.3.1 Components of the Decision Theory

1.3.2 Bayes and Minimax Criteria

1.4 Prediction

1.5 Sufficiency

1.6 Exponential Families

1.6.1 The One-Parameter Case

1.6.2 The Multiparameter Case

1.6.3 Properties of Exponential Families

1.6.4 Conjugate Families of Prior Distributions

1.7 Exercises

2 Methods of Parameter Estimation

2.1 Essentials of Point Estimation

2.1.1 M-Estimation

2.1.2 The Substitution Principle

2.2 Least" Squares and Maximum Likelihood Methods

2.2.1 Least Squares and Weighted Least Squares Estimation

2.2.2 Maximum Likelihood Estimation

2.3 The MLE in Expcnential Families

2.4 Algorithmic Issues for Parameter Estimation

2.4.1 The Bisection Method

2.4.2 The Coordinate Ascent Method

2.4.3 The Newton-Raphson Algorithm

2.4.4 The EM Algorithm

2.5 Exercises

3 Measures of Performance and Optimality

3.1 Bayes Principle

3.2 Minimax Principle

3.3 Unbiased Estimation

3.4 Tl~e Information Inequality

3.4.1 The One-Parameter Case

3.4.2 The Multiparameter Case

3.5 Exercises

4 Hypothesis Tests and Confidence Regions

4.1 The Framework of Hypothesis Testing

4.2 The Neyman-Pearson Test

4.3 Uniformly Mast Powerful Tests

4.4 Ccnfidence Intervals and Regions

4.5 The Duality between Confidence Regions and Hypothesis Tests

4.6 Uniformly Mast Accurate Ccnfidence Bounds

4.7 Bayesian Formulation of Credible Regions

4.8 Prediction Intervals

4.9 Likelihood Ratio Tests

4.9.1 Introduction

4.9.2 One-Sample Problem for a Normal Distribution

4.9.3 Two-Sample Problem with Equal Variance

4.9.4 Two-Sample Problem with Unequal Variances

4.9.5 Likelihood Ratio Tests for Bivariate Normal Distributions

4.10 Exercises

5 Asymptotic Theories

5.1 Introduction

5.2 Consistency

5.2.1 Consistency in Estimation

5.2.2 Consistency of M-Estimates

5.3 Asymptotics Based on the Delta Method

5.3.1 The Delta Method for Approximations of Moments

5.3.2 The Delta Method for Approximations of Distributions

5.4 Asymptotic Theory in One Dimension

5.4.1 Asymptotic Normality of M-Estimates

5.4.2 Asymptotic Normality and Efficiency of MLEs

5.4.3 One-Sided Tests and Confidence Intervals Based on the MLE

5.5 Asymptotic Theory of the Posterior Distribution

5.6 Exercises

6 Asymptotics in the Multiparameter Case

6.1 Asymptotic Normality in k Dimensions

6.1.1 Asymptotic Normality of M-Estimates

6.1.2 Asymptotic Normality and Efficiency of MLEs

6.2 Large-Sample Tests and Confidence Regions

6.2.1 Asymptotic Distribution of the Likelihood-Ratio Test Statistic

6.2.2 Wald's and Rao's Large-Sample Tests and Confidence Regions

6.3 Large-Sample Tests for Categorical Data

6.3.1 Goodness-of-Fit Tests for Multinomial Models

6.3.2 Goodness-of-Fit Tests for Composite Multinomial Models

6.3.3 The X2 Tests for Contingency Tables

6.4 Exercises

Appendix A: Table of Common Distributions

Appendix B: Statistical Tables

Table 1. The Standard Normal Distribution

Table 2. Distribution of t

Table 3. Distribution of X2

Table 4. Distribution of F

References

Index

内容摘要:

《数理统计(英文版)(Mathematical Statistics)》是作者根据多年在国内外高校从事教学和科研的经验,专门为英语为非母语的读者精细撰写的英文专著,系统而简明地介绍了《数理统计》的基本方法和理论,并配有适量精选的习题供读者练习。
  《数理统计(英文版)(Mathematical Statistics)》共分6章,内容包括:统计数据与模型、参数估计方法、优良性准则、假设检验与置信区域、渐近性理论及多参数渐近性理论。

书籍规格:

书籍详细信息
书名数理统计站内查询相似图书
9787030374097
如需购买下载《数理统计》pdf扫描版电子书或查询更多相关信息,请直接复制isbn,搜索即可全网搜索该ISBN
出版地北京出版单位科学出版社
版次1版印次1
定价(元)37.0语种英文
尺寸24 × 17装帧平装
页数 232 印数

书籍信息归属:

数理统计是科学出版社于2013.出版的中图分类号为 O212 的主题关于 数理统计-英文 的书籍。