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January, 1978 Latent Roots and Matrix Variates: A Review of Some Asymptotic Results
Robb J. Muirhead
Ann. Statist. 6(1): 5-33 (January, 1978). DOI: 10.1214/aos/1176344063


The exact noncentral distributions of matrix variates and latent roots derived from normal samples involve hypergeometric functions of matrix argument. These functions can be defined as power series, by integral representations, or as solutions of differential equations, and there is no doubt that these mathematical characterizations have been a unifying influence in multivariate noncentral distribution theory, at least from an analytic point of view. From a computational and inference point of view, however, the hypergeometric functions are themselves of very limited value due primarily to the many difficulties involved in evaluating them numerically and consequently in studying the effects of population parameters on the distributions. Asymptotic results for large sample sizes or large population latent roots have so far proved to be much more useful for such problems. The purpose of this paper is to review some of the recent results obtained in these areas.


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Robb J. Muirhead. "Latent Roots and Matrix Variates: A Review of Some Asymptotic Results." Ann. Statist. 6 (1) 5 - 33, January, 1978.


Published: January, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0375.62050
MathSciNet: MR458719
Digital Object Identifier: 10.1214/aos/1176344063

Primary: 62H10
Secondary: 62E20

Keywords: Asymptotic distributions , canonical correlations , discriminant analysis , hypergeometric functions , latent roots , matrix variates , noncentral means , principal components

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 1 • January, 1978
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