Aspects of multivariate statistical theory
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.
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THE MULTIVARIATE NORMAL AND RELATED DISTRIBUTIONS
JACOBIANS EXTERIOR PRODUCTS KRONECKER PRODUCTS
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_j _ 2plog asymptotic distribution characteristic function CK(Y columns Corollary defined denotes distribution function elliptical distribution exterior product following theorem gives group of transformations H'dH Hence hypergeometric functions hypothesis H independent integral invariant under G Jacobian joint density function Lemma likelihood function likelihood ratio statistic likelihood ratio test linear loss function maximal invariant maximum likelihood estimate modified likelihood ratio multiple correlation coefficient multivariate normal distribution mXm matrix Nm(p nonsingular nonzero latent roots Note null distribution null hypothesis obtained orthogonal matrix partition positive definite powerful invariant test ppppp ppppp principal components problem proof is complete proof of Theorem prove random variables random vectors rejects H sample covariance matrix Section Show sufficient statistic Suppose symmetric function symmetric matrix test statistics testing H testing the null tion uniformly most powerful upper-triangular variance Wishart distribution Wm(n zero zonal polynomials