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 |
SAMPLES FROM A MULTIVARIATE NORMAL DISTRIBUTION | 79 |
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A₁ asymptotic distribution B₁ characteristic function Corollary denotes distribution function elliptical distribution F₁ following theorem function of 2plog given gives group of transformations H is true H₁ H₂ Hence hypergeometric functions hypothesis H independent integral invariant under G joint density function Laplace transform Lemma likelihood function likelihood ratio statistic likelihood ratio test M₁ m₂ maximal invariant modified likelihood ratio multivariate n₁ n₂ noncentral normal distribution Note null distribution null hypothesis obtained orthogonal orthogonal matrix P₁ parameter partition positive definite principal components problem proof is complete random variables random vectors rejects H sample covariance matrix Section shows sufficient statistic Suppose symmetric function symmetric matrix test statistics testing H testing the null Theorem uniformly most powerful V₁ variance Wishart distribution X₁ Y₁ zonal polynomials Σ Σ