Aspects Of Multivariate Statistical Theory

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". . . 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.

ROBB J. MUIRHEAD, PhD, is Professor in the Department of Statistics at the University of Michigan. He received his PhD in 1970 from the University of Adelaide in Australia.

Tables.

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.

Bibliography.

Index.