实用多元统计分析（第6版）

    书籍
    数学书籍
多元统计分析是统计学中内容十分丰富、应用范围极为广泛的一个分支。在自然科学和社会科学的许多学科中，研究者都有可能需要分析处理有多个变量的数据的问题。能否从表面上看起来杂乱无章的数据中发现和提炼出规律性的结论，不仅需要对所研究的专业领域有很好的训练，而且要掌握必要的统计分析工具。
对研究者来说，本书是学习掌握多元统计分析的各种模型和方法的一本有价值的参考书：首先，它做到了“浅入深出”，既可供初学者入门，又能使有较深基础的人受益；其次，它既侧重于应用，又兼顾必要的推理论证，使学习者既能学到“如何”做，又能在一定程度上了解“为什么” 这样做；最后，它内涵丰富、全面，不仅基本包括各种在实际中常用的多元统计分析方法，而且对现代统计学的最新思想和进展有所介绍。值得一提的是，本书中有大量来自实际问题的数据实例，通过对这些实例的分析，读者可以学到如何将一个实际问题转化为恰当的统计问题，进而选择恰当的方法来进行分析。

第1章 多元分析概述
　1.1 引言
　1.2 多元方法的应用
　1.3 数据的组织
　1.4 数据的展示及图表示
　1.5 距离
　1.6 最终评注
第2章 矩阵代数与随机向量
　2.1 引言
　2.2 矩阵和向量代数基础
　2.3 正定矩阵
　2.4 平方根矩阵
　2.5 随机向量和矩阵
　2.6 均值向量和协方差矩阵
　2.7 矩阵不等式和极大化
　补充2A 向量与矩阵：基本概念
第3章 样本几何与随机抽样
　3.1 引言
　3.2 样本几何
　3.3 随机样本以及样本均值和协方差矩阵的期望值

　　INTENDED AUDIENCE .
　　This book originally grew out of our lecture notes for an "Applied Multivariate Analysis" course offered jointly by the Statistics Department and the School of Business at the University of Wisconsin-Madison. Applied Multivariate Statisti-cal Analysis, Sixth Edition, is concerned with statistical methods for describing and analyzing multivariate data. Data analysis, while interesting with one variable, becomes truly fascinating and challenging when several variables are involved. Researchers in the biological, physical, and social sciences frequently collect measurements on several variables. Modern computer packages readily provide the numerical results to rather complex statistical analyses. We have tried to provide readers with the supporting knowledge necessary for making proper interpretations, selecting appropriate techniques, and understanding their strengths and weaknesses. We hope our discussions will meet the needs of experimental scientists, in a wide variety of subject matter areas, as a readable introduction to the statistical analysis of multivariate observations.
　　LEVEL
　　Our aim is to present the concepts and methods of multivariate analysis at a level that is readily understandable by readers who have taken two or more statistics courses. We emphasize the applications of multivariate methods and, consequently, have attempted to make the mathematics as palatable as possible. We avoid the use of calculus. On the other hand, the concepts of a matrix and of matrix manipulations are important. We do not assume the reader is familiar with matrix algebra. Rather, we introduce matrices as they appear naturally in our discussions, and we then show how they simplify the presentation of multivariate models and techniques.
　　The introductory account of matrix algebra, in Chapter 2, highlights the more important matrix algebra results as they apply to multivariate analysis. The Chapter 2 supplement provides a summary of matrix algebra results for those with little or no previous exposure to the subject. This supplementary material helps make the book self-contained and is used to complete proofs. The proofs may be ignored on the first reading. In this way we hope to make the book accessible to a wide audience.
　　In our attempt to make the study of multivariate analysis appealing to a large audience of both practitioners and theoreticians, we have had to sacrifice a consistency of level. Some sections are harder than others. In particular, we have summarized a voluminous amount of material on regression in Chapter 7. The resulting presentation is rather succinct and difficult the first time through. We hope instructors will be able to compensate for the unevenness in level by judiciously choosing those sections, and subsections, appropriate for their students and by toning them down if necessary.
　　ORGANIZATION AND APPROACH
　　The methodological "tools" of multivariate analysis are contained in Chapters 5 through 12. These chapters represent the heart of the book, but they cannot be assimilated without much of the material in the introductory Chapters ! through 4. Even those readers with a good knowledge of matrix algebra or those willing to accept the mathematical results on faith should, at the very least, peruse Chapter 3, "Sample Geometry," and Chapter 4, "Multivariate Normal Distribution."
　　Our approach in the methodological chapters is to keep the discussion direct and uncluttered. Typically, we start with a formulation of the population models, delineate the corresponding sample results, and liberally illustrate everything with examples. The examples are of two types: those that are simple and whose calculations can be easily done by hand, and those that rely on real-world data and computer software. These will provide an opportunity to (1) duplicate our analyses, (2) carry out the analyses dictated by exercises, or (3) analyze the data using methods other than the ones we have used or suggested.
　　The division of the methodological chapters (5 through 12) into three units allows instructors some flexibility in tailoring a course to their needs. Possible sequences for a one-semester (two quarter) course are indicated schematically.
　　Each instructor will undoubtedly omit certain sections from some chapters to cover a broader collection of topics than is indicated by these two choices.
　　For most students, we would suggest a quick pass through the first four chapters (concentrating primarily on the material in Chapter 1; Sections 2.1,2.2, 2.3, 2.5, 2.6, and 3.6; and the "assessing normality" material in Chapter 4) followed by a selection of methodological topics. For example, one might discuss the comparison of mean vectors, principal components, factor analysis, discriminant analysis and clustering. The discussions could feature the many "worked out" examples included in these sections of the text. Instructors may rely on diagrams and verbal descriptions to teach the corresponding theoretical developments. If the students have uniformly strong mathematical backgrounds, much of the book can successfully be covered in one term. ..
　　We have found individual data-analysis projects useful for integrating material from several of the methods chapters. Here, our rather complete treatments of multivariate analysis of variance (MANOVA), regression analysis, factor analysis, canonical correlation, discriminant analysis, and so forth are helpful, even though they may not be specifically covered in lectures.
　　CHANGES TO THE SIXTH EDITION
　　New material. Users of the previous editions will notice several major changes in the sixth edition.
　　Twelve new data sets including national track records for men and women, psychological profile scores, car body assembly measurements, cell phone tower breakdowns, pulp and paper properties measurements, Mali family farm data, stock price rates of return, and Concho water snake data.
　　Thirty seven new exercises and twenty revised exercises with many of these exercises based on the new data sets.
　　Four new data based examples and fifteen revised examples.
　　Six new or expanded sections:
　　1. Section 6.6 Testing for Equality of Covariance Matrices