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September, 1980 Asymptotic Representations of the Densities of Canonical Correlations and Latent Roots in MANOVA When the Population Parameters Have Arbitrary Multiplicity
William J. Glynn
Ann. Statist. 8(5): 958-976 (September, 1980). DOI: 10.1214/aos/1176345135

Abstract

Asymptotic representations of the joint densities of the canonical correlation coefficients, calculated from a sample from a multivariate normal population, and of the latent roots of $B(B + W)^{-1},$ where $B$ is $W_p(n_1, \Sigma, \Omega)$ and $W$ is $W_p(n_2, \Sigma),$ are obtained by deriving asymptotic representations of the hypergeometric functions in the joint densities. The results hold in the first case for large sample size and arbitrary values of the population canonical correlations and in the second case for large $n_2$ and $\Omega = n_2\Theta,$ where the latent roots of the noncentrality matrix $\Omega$ are arbitrary.

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William J. Glynn. "Asymptotic Representations of the Densities of Canonical Correlations and Latent Roots in MANOVA When the Population Parameters Have Arbitrary Multiplicity." Ann. Statist. 8 (5) 958 - 976, September, 1980. https://doi.org/10.1214/aos/1176345135

Information

Published: September, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0508.62019
MathSciNet: MR585696
Digital Object Identifier: 10.1214/aos/1176345135

Subjects:
Primary: 62E20
Secondary: 62H10 , 62H15 , 62H20

Keywords: Asymptotic representation , canonical correlations , hypergeometric functions , latent roots , MANOVA

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 5 • September, 1980
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