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July, 1975 Asymptotic Expansions for the Joint and Marginal Distributions of the Latent Roots of the Covariance Matrix
R. J. Muirhead, Y. Chikuse
Ann. Statist. 3(4): 1011-1017 (July, 1975). DOI: 10.1214/aos/1176343205

Abstract

Let nS be an $m\times m$ matrix having the Wishart distribution $W_m(n,\Sigma)$. For large n and simple latent roots of $\Sigma$, it is known that the latent roots of S are asymptotically independently normal. In this paper an expansion, up to and including the terms of order $n^-1$, is given for the joint density function of the roots of S in terms of normal density functions. Expansions for the marginal distributions of the roots are also given, valid when the corresponding roots of $\Sigma$ are simple.

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R. J. Muirhead. Y. Chikuse. "Asymptotic Expansions for the Joint and Marginal Distributions of the Latent Roots of the Covariance Matrix." Ann. Statist. 3 (4) 1011 - 1017, July, 1975. https://doi.org/10.1214/aos/1176343205

Information

Published: July, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0311.62023
MathSciNet: MR395046
Digital Object Identifier: 10.1214/aos/1176343205

Subjects:
Primary: 62H10
Secondary: 35B40 , 41A60 , 62E20

Keywords: asymptotic expansions , Covariance matrix , latent roots , Wishart distribution

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 4 • July, 1975
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