The Annals of Statistics

Asymptotic Expansions for the Joint and Marginal Distributions of the Latent Roots of the Covariance Matrix

R. J. Muirhead and Y. Chikuse

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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.

Article information

Source
Ann. Statist., Volume 3, Number 4 (1975), 1011-1017.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343205

Digital Object Identifier
doi:10.1214/aos/1176343205

Mathematical Reviews number (MathSciNet)
MR395046

Zentralblatt MATH identifier
0311.62023

JSTOR
links.jstor.org

Subjects
Primary: 62H10: Distribution of statistics
Secondary: 62E20: Asymptotic distribution theory 35B40: Asymptotic behavior of solutions 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]

Keywords
Wishart distribution latent roots covariance matrix asymptotic expansions

Citation

Muirhead, R. J.; Chikuse, Y. Asymptotic Expansions for the Joint and Marginal Distributions of the Latent Roots of the Covariance Matrix. Ann. Statist. 3 (1975), no. 4, 1011--1017. doi:10.1214/aos/1176343205. https://projecteuclid.org/euclid.aos/1176343205


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