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General Moments of the Inverse Real Wishart Distribution and Orthogonal Weingarten Functions

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  • Sho Matsumoto

    (Nagoya University)

Abstract

We study a random positive definite symmetric matrix distributed according to a real Wishart distribution. We compute general moments of the random matrix and of its inverse explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study of Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.

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  • Sho Matsumoto, 2012. "General Moments of the Inverse Real Wishart Distribution and Orthogonal Weingarten Functions," Journal of Theoretical Probability, Springer, vol. 25(3), pages 798-822, September.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:3:d:10.1007_s10959-011-0340-0
    DOI: 10.1007/s10959-011-0340-0
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    References listed on IDEAS

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    1. Letac, Gérard & Massam, Hélène, 2008. "The noncentral Wishart as an exponential family, and its moments," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1393-1417, August.
    2. Satoshi Kuriki & Yasuhide Numata, 2010. "Graph presentations for moments of noncentral Wishart distributions and their applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 645-672, August.
    3. P. Graczyk & G. Letac & H. Massam, 2005. "The Hyperoctahedral Group, Symmetric Group Representations and the Moments of the Real Wishart Distribution," Journal of Theoretical Probability, Springer, vol. 18(1), pages 1-42, January.
    4. Gérard Letac & Hélène Massam, 2004. "All Invariant Moments of the Wishart Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 295-318, June.
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    Cited by:

    1. Bavaud, François, 2023. "Exact first moments of the RV coefficient by invariant orthogonal integration," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

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