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 | 76 |
Copyright | |
18 other sections not shown
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Common terms and phrases
2plog alternatives argument assume asymptotic distribution called canonical Chapter characteristic function complete conditional consider constant Corollary correlation coefficient corresponding covariance matrix defined denotes density function depends derived differential equations elements equal equivalent estimate example expansion expressed fact following theorem given gives Hence hypothesis H independent integral invariant invariant test latent roots Lemma likelihood ratio statistic likelihood ratio test maximal invariant maximum mean moments multiple multivariate n₁ n₂ noncentral normal normal distribution Note null hypothesis obtained orthogonal orthogonal matrix parameter partition population positive definite powerful problem Proof properties prove rank reader referred rejects H relation respect result sample satisfies Section shows side space Suppose symmetric symmetric matrix tion transformations true unique upper values variance write zonal polynomials Σ Σ