Aspects of Multivariate Statistical TheoryThe 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. |
Contents
THE MULTIVARIATE NORMAL AND RELATED DISTRIBUTIONS | 1 |
JACOBIANS EXTERIOR PRODUCTS KRONECKER PRODUCTS | 50 |
Problems | 112 |
Copyright | |
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2plog alternatives analysis assume asymptotic distribution called canonical characteristic function columns complete conditional consider Corollary correlation coefficient corresponding covariance matrix defined denotes density function depends derived differential elements elliptical equal equation estimate exists expansion expressed fact following theorem given gives Hence independent integral invariant joint density function largest latent roots Lemma likelihood ratio statistic likelihood ratio test linear loss maximum mean moments multiple multivariate n₁ n₂ noncentral normal normal distribution Note null hypothesis obtained orthogonal orthogonal matrix parameter partition population positive definite principal components probability problem Proof prove rank reader referred respect result sample satisfies Section Show side Suppose symmetric symmetric matrix Table tion transformations true upper values variables variance write zero zonal polynomials