Skip to main content

Aspects of Multivariate Statistical Theory

Aspects of Multivariate Statistical Theory

Robb J. Muirhead

ISBN: 978-0-470-31670-2

Sep 2009

704 pages



The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.

". . . the wealth of material on statistics concerning the multivariate normal distribution is quite exceptional. As such it is a very useful source of information for the general statistician and a must for anyone wanting to penetrate deeper into the multivariate field."
-Mededelingen van het Wiskundig Genootschap

"This book is a comprehensive and clearly written text on multivariate analysis from a theoretical point of view."
-The Statistician

Aspects of Multivariate Statistical Theory presents a classical mathematical treatment of the techniques, distributions, and inferences based on multivariate normal distribution. Noncentral distribution theory, decision theoretic estimation of the parameters of a multivariate normal distribution, and the uses of spherical and elliptical distributions in multivariate analysis are introduced. Advances in multivariate analysis are discussed, including decision theory and robustness. The book also includes tables of percentage points of many of the standard likelihood statistics used in multivariate statistical procedures. This definitive resource provides in-depth discussion of the multivariate field and serves admirably as both a textbook and reference.

Commonly Used Notation.

1. The Multivariate Normal and Related Distributions.

2. Jacobians, Exterior Products, Kronecker Products, and Related Topics.

3. Samples from a Multivariate Normal Distribution, and the Wishart and Multivariate BETA Distributions.

4. Some Results Concerning Decision-Theoretic Estimation of the Parameters of a Multivariate Normal Distribution.

5. Correlation Coefficients.

6. Invariant Tests and Some Applications.

7. Zonal Polynomials and Some Functions of Matrix Argument.

8. Some Standard Tests on Covariance Matrices and Mean Vectors.

9. Principal Components and Related Topics.

10. The Multivariate Linear Model.

11. Testing Independence Between k Sets of Variables and Canonical Correlation Analysis.

Appendix: Some Matrix Theory.