In the preparation of this book, my objectives were the following:
1. To provide a theoretical foundation for multivariate analysis at an accessible level. I have searched for or devised proofs that are easy to follow for students with a minimum of theoretical background in statistics. For some readers, these proofs are an essential part of understanding the material and furnish insights obtainable in no other way. Others may wish to skip the proofs on a first reading.
2. To cover a wide range of areas of application. The book is driven by applications in its choice of topics and its choice of literature to cite. I have carefully selected new developments that can be applied, not those of theoretical interest only.
3. To provide a comprehensive survey of the literature in multivariate analysis. The bibliography in this book has over 900 entries and is fairly comprehensive (I have listed only these references cited in the text). In addition to providing original sources for fundamental techniques, I have combed the multivariate literature for the past 20 years and have included most developments that appear to have potential for application. In the classroom setting, these recent citations will provide sources for miniprojects. As a reference book, the statistical researcher will find definitive original sources, and the practitioner will gain access to methodological details and algorithms for applying the latest useful techniques.
4. Above all else, to provide clarity of exposition. I hope that students, instructors, researchers, and practitioners alike will find this book more comfortable than most.
The mathematical prerequisites for this book are calculus and matrix algebra. Statistical prerequisites include some exposure to statistical theory, including distributions of random variables, expected values, moment-generating functions, and an introduction to estimation and testing hypotheses. One or two statistical methods courses would also be helpful, with coverage of basic procedures such as \(t\)-tests, regression analysis, and analysis of variance.
The book provides a substantial number of theoretical problems and a smaller number of applied problems using real data sets. The problems, along with the answers in Appendix C, extend the book in two significant ways: (1) the theoretical problems and anwers fill in nearly all gaps in derivations and proofs and also extend the coverage of material in the text and (2) the numerical problems and answers extend the examples illustrating the theory.
The Diskette that accompanies the book contains the following: 1. All the data sets, including those referred to but not shown in the text. 2. SAS command files for all the examples in the text. 3. SAS command files for all the numerical problems in the text. 4. An annotated example introducing SAS IML. (From the preface)
Contents (Chapter headings): 1. Some properties of random vectors and matrices; 2. The multivariate normal distribution; 3. Hotelling’s \(T^2\)-tests; 4. Multivariate analysis of variance; 5. Discriminant functions for descriptive group separation; 6. Classification of observations into groups; 7. Multivariate regression; 8. Canonical correlation; 9. Principal component analysis; 10. Factor analysis. Appendices: A. Review of matrix algebra; B. Tables; C. Answers and hints to selected problems. Bibliography. Index.