Open Access
Translator Disclaimer
July, 1976 Maximization of an Integral of a Matrix Function and Asymptotic Expansions of Distributions of Latent Roots of Two Matrices
A. K. Chattopadhyay, K. C. S. Pillai, Hung C. Li
Ann. Statist. 4(4): 796-806 (July, 1976). DOI: 10.1214/aos/1176343554

Abstract

The noncentral distribution of latent roots arising in several situations in multivariate analysis involves the integration of a hypergeometric function of matrix variates over a group of orthogonal matrices in the real case and that of unitary matrices in the complex case. In this paper the subgroup of the orthogonal group (unitary group) for which the integrand is maximized has been found under mild restrictions. The results of earlier authors (Anderson, Chang, James, Li and Pillai) follow as special cases. Further, the maximization results concerning the integrand have been used to study asymptotic expansions of the distributions of the characteristic roots of matrices arising in canonical correlation analysis and MANOVA when the corresponding parameter matrices have several multiple roots.

Citation

Download Citation

A. K. Chattopadhyay. K. C. S. Pillai. Hung C. Li. "Maximization of an Integral of a Matrix Function and Asymptotic Expansions of Distributions of Latent Roots of Two Matrices." Ann. Statist. 4 (4) 796 - 806, July, 1976. https://doi.org/10.1214/aos/1176343554

Information

Published: July, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0345.62039
MathSciNet: MR428592
Digital Object Identifier: 10.1214/aos/1176343554

Subjects:
Primary: 62H10

Keywords: asymptotic expansions , Canonical correlation , characteristic roots , distribution , integral of a matrix function , MANOVA , Maximization , several multiple population roots

Rights: Copyright © 1976 Institute of Mathematical Statistics

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.4 • No. 4 • July, 1976
Back to Top