The Annals of Statistics

Latent Roots and Matrix Variates: A Review of Some Asymptotic Results

Robb J. Muirhead

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 6, Number 1 (1978), 5-33.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344063

Digital Object Identifier
doi:10.1214/aos/1176344063

Mathematical Reviews number (MathSciNet)
MR458719

Zentralblatt MATH identifier
0375.62050

JSTOR
links.jstor.org

Subjects
Primary: 62H10: Distribution of statistics
Secondary: 62E20: Asymptotic distribution theory

Keywords
Latent roots matrix variates asymptotic distributions hypergeometric functions principal components noncentral means discriminant analysis canonical correlations

Citation

Muirhead, Robb J. Latent Roots and Matrix Variates: A Review of Some Asymptotic Results. Ann. Statist. 6 (1978), no. 1, 5--33. doi:10.1214/aos/1176344063. https://projecteuclid.org/euclid.aos/1176344063


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