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Februrary 2003 The complex Wishart distribution and the symmetric group
Piotr Graczyk, Gérard Letac, Hélène Massam
Ann. Statist. 31(1): 287-309 (Februrary 2003). DOI: 10.1214/aos/1046294466

Abstract

Let V be the space of (r,r) Hermitian matrices and let $\Omega$ be the cone of the positive definite ones. We say that the random variable S, taking its values in $\overline{\Omega},$ has the complex Wishart distribution $\gamma_{p,\sigma}$ if $\mathbb{E}(\exp \,\tr (\theta S))=(\det (I_r-\sigma\theta))^{-p},$ where $\sigma$ and $\sigma^{-1}-\theta$ are in $\Omega,$ and where p=1,2,...,r-1 or p>r-1. In this paper, we compute all moments of $S$ and $S^{-1}.$ The techniques involve in particular the use of the irreducible characters of the symmetric group.

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Piotr Graczyk. Gérard Letac. Hélène Massam. "The complex Wishart distribution and the symmetric group." Ann. Statist. 31 (1) 287 - 309, Februrary 2003. https://doi.org/10.1214/aos/1046294466

Information

Published: Februrary 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1019.62047
MathSciNet: MR1962508
Digital Object Identifier: 10.1214/aos/1046294466

Subjects:
Primary: 62H05
Secondary: 60E05, 62E17

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 1 • Februrary 2003
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