Comprehensive Reference Work on Multivariate Analysis and its Applications
The first edition of this book, by Mardia, Kent and Bibby, has been used globally for over 40 years. This second edition brings many topics up to date, with a special emphasis on recent developments.
A wide range of material in multivariate analysis is covered, including the classical themes of multivariate normal theory, multivariate regression, inference, multidimensional scaling, factor analysis, cluster analysis and principal component analysis. The book also now covers modern developments such as graphical models, robust estimation, statistical learning, and high-dimensional methods. The book expertly blends theory and application, providing numerous worked examples and exercises at the end of each chapter. The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are appendices which provide a background in matrix algebra, a summary of univariate statistics, a collection of statistical tables and a discussion of computational aspects. The work includes coverage of: - Basic properties of random vectors, copulas, normal distribution theory, and estimation - Hypothesis testing, multivariate regression, and analysis of variance - Principal component analysis, factor analysis, and canonical correlation analysis - Discriminant analysis, cluster analysis, and multidimensional scaling - New advances and techniques, including supervised and unsupervised statistical learning, graphical models and regularization methods for high-dimensional data
Although primarily designed as a textbook for final year undergraduates and postgraduate students in mathematics and statistics, the book will also be of interest to research workers and applied scientists.
Table of Contents
Epigraph xvii
Preface to the Second Edition xix
Preface to the First Edition xxi
Acknowledgments from First Edition xxv
Notation, Abbreviations, and Key Ideas xxvii
1 Introduction 1
2 Basic Properties of Random Vectors 25
3 Nonnormal Distributions 49
4 Normal Distribution Theory 71
5 Estimation 101
6 Hypothesis Testing 125
7 Multivariate Regression Analysis 159
8 Graphical Models 183
9 Principal Component Analysis 207
10 Factor Analysis 259
11 Canonical Correlation Analysis 281
12 Discriminant Analysis and Statistical Learning 297
13 Multivariate Analysis of Variance 355
14 Cluster Analysis and Unsupervised Learning 379
15 Multidimensional Scaling 419
16 High-dimensional Data 449
A Matrix Algebra 475
B Univariate Statistics 505
C R Commands and Data 509
D Tables 513
References and Author Index 523
Index 543
