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. |
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A₁ asymptotic distribution asymptotic expansion B₁ characteristic function Corollary defined denotes distribution function elliptical distribution exterior product following theorem function of 2plog given gives H is true H₁ H₂ Hence hypergeometric functions hypothesis H independent integral joint density function Lemma likelihood function likelihood ratio statistic likelihood ratio test linear M₁ maximal invariant maximum likelihood estimate modified likelihood ratio multiple correlation coefficient multivariate analysis multivariate normal distribution n₁ n₂ noncentral nonsingular normal distribution Note null distribution null hypothesis obtained orthogonal matrix P₁ partition Pillai positive definite principal components problem proof is complete random variables random vectors reject H sample covariance matrix Section Show Suppose test statistics testing H testing the null Theorem uniformly most powerful upper-triangular variance Wishart distribution X₁ x²m Y₁ zero zonal polynomials Σ Σ