### 基本信息

- 原书名：Mathematical Statistics and Data Analysis,Second Edition
- 原出版社： Thomson

### 内容简介

数学书籍

本书将现代统计学的重要思想引入数理统计课程中，强调了数据分析。图形工具和计算机技术，反映出计算机在统计学中扮演着越来越重要的角色。为了说明数理统计在统计实践和科学研究中所起的作用。

本书用真实数据分析了实际问题，以此增强读者对理论的理解； 作者将bootstrap方法与传统的推论性过程结合起来，增加了蒙特卡罗方法，此外，为了使概念更清晰，书中提供了大量的示例，而且还有丰富的习题，以增强读者的计算能力。

本书适合作为统计学。数学。其他理工科专业以及社会科学和经济学专业的高年级本科生和低年级研究生的教材，同时也可供相关领域技术人员参考。

欢迎下载随书赠送的软盘内容：http://images.china-pub.com/ebook10000-15000/13108/1.rar

### 作译者

### 目录

2 随机变量

3 联合分布

4 期望值

5 极限定理

6 普通分布的导出分布

7 抽样调查

8 参数估计与概率分布拟合

9 假设检验及拟合优点评估

10 数据汇总

11 比较两个样本

12 变量分析

13 分类数据分析

14 线性最小二乘法

15 决策论及贝叶斯推论

### 前言

This text is intended for juniors, seniors, or beginning graduate students in statistics, mathematics, natural sciences, and engineering as well as for ade-quately prepared students in the social sciences and economics. A year of calculus, including Taylor Series and multivariable calculus, and an introduc-tory course in linear algebra are prerequisites.

This Book's Objectives

This book reflects my view of what a first, and for many students last, course in

statistics should be. Such a course should include some traditional topics in mathematical statistics (such as methods based on likelihood), topics in descrip-tive statistics and data analysis with special attention to graphical displays,aspects of experimental design, and realistic applications of some complexity.It should also reflect the quickly growing use of computers in statistics. These themes, properly interwoven, can give students a view of the nature of modern statistics. The alternative of teaching two separate courses, one on theory and one on data analysis, seems to me artificial. Furthermore, many students take only one course in statistics and do not have time for two or more.

Analysis of Data and the Practice of Statistics

In order to draw the above themes together, I have endeavored to write a book closely tied to the practice of statistics. It is in the analysis of real data that one sees the roles played by both formal theory and informal data analytic methods.I have organized this book around various kinds of problems that entail the use of statistical methods and have included many real examples to motivate and introduce the theory. Among the advantages of such an approach are that

theoretical constructs are presented in meaningful contexts, that they are grad-ally supplemented and reinforced, and that they are integrated with more informal methods. This is, I think, a fitting approach to statistics, the historical development of which has been spurred on primarily by practical needs rather than abstract or aesthetic considerations. At the same time, I have not shied away from using the mathematics that the students are supposed to know.

This Revision

The basic intent and structure of the book remain the same. In composing the second edition, I have focused my efforts in two areas: improving the existing material pedagogically and incorporating new material. Thus, in the first area,I have expanded and revised discussions where I thought the existing discussion too terse, and I have included new examples in the text where I thought they would be helpful to the reader. For example, I have revised the introduction of

confidence intervals in Chapter 7 and their reintroduction in Chapter 8. The introduction of the Mann-Whitney test in Chapter 11 has been rewritten in order to make the ideas clearer. More than 150 new problems have been added. In particular, to help students check their comprehension, these include a large number of routine exercises, such as true-false questions. Some more advanced problems have been added as well. One of the most influential developments in statistics in the last decade has been the introduction and rapid dissemination of bootstrap methods. This devel-opment is of such fundamental importance that, to my mind, its inclusion in an introductory course at the level of this text is mandatory. I introduce the boot-strap in Chapter 8, where the parametric bootstrap arises quite naturally. As well as being of great practical importance, introduction of the bootstrap at this point reinforces the concept of a sampling distribution. The nonparametric bootstrap is introduced in Chapter 10 in the context of estimating the standard error of a location estimate. It arises again in Chapter 11 as a method for assessing the variability of a shift estimate, in Chapter 13 for assessing the variability of the estimate of an odds ratio (a new section of Chapter 13 is devoted to the odds ratio), and finally in Chapter 14 in a discussion of the "random X model" for regression. New problems throughout these chapters ask students how to use the bootstrap to estimate standard errors and confidence intervals for various functionals.

Brief Outline

A complete outline can be found, of course, in the table of contents. Here I will just highlight some points and indicate various curricular options for the instructor.

The first six chapters contain an introduction to probability theory, particu-larly those aspects most relevant to statistics. Chapter 1 introduces the basic ingredients of probability theory and elementary combinatorial methods from a non-measure theoretic point of view. In this and the other probability chapters,I have tried to use real-world examples rather than balls and urns wheneverpossible.

The concept of a random variable is introduced in Chapter 2. I chose to discuss discrete and continuous random variables together, instead of putting off the continuous case until later. Several common distributions are introduced.An advantage of this approach is that it provides something to work with anddevelop in later chapters.

Chapter 3 continues the treatment of random variables by going into joint distributions. The instructor may wish to skip lightly over Jacobians; this can be done with little loss of continuity, since they are utilized rarely in the rest of the book. The material in Section 3.7 on extrema and order statistics can be omitted if the instructor is willing to do a little backtracking later.

Expectation, variance, covariance, conditional expectation, and moment-generating functions are taken up in Chapter 4. The instructor may wish to pass lightly over conditional expectation and prediction, especially if he or she does not plan to cover sufficiency later. The last section of this chapter introduces the method, or the method of propagation of error. This method is used several times in the statistics chapters.