The Annals of Statistics

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, and Hung C. Li

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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.

Article information

Source
Ann. Statist., Volume 4, Number 4 (1976), 796-806.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343554

Digital Object Identifier
doi:10.1214/aos/1176343554

Mathematical Reviews number (MathSciNet)
MR428592

Zentralblatt MATH identifier
0345.62039

JSTOR
links.jstor.org

Subjects
Primary: 62H10: Distribution of statistics

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

Citation

Chattopadhyay, A. K.; Pillai, K. C. S.; Li, Hung C. Maximization of an Integral of a Matrix Function and Asymptotic Expansions of Distributions of Latent Roots of Two Matrices. Ann. Statist. 4 (1976), no. 4, 796--806. doi:10.1214/aos/1176343554. https://projecteuclid.org/euclid.aos/1176343554


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