The noncentral Wishart as an exponential family, and its moments

Gérard Letac and Hélène Massam

Journal of Multivariate Analysis, 2008, vol. 99, issue 7, 1393-1417

Abstract: While the noncentral Wishart distribution is generally introduced as the distribution of the random symmetric matrix where Y1,...,Yn are independent Gaussian rows in with the same covariance, the present paper starts from a slightly more general definition, following the extension of the chi-square distribution to the gamma distribution. We denote by [gamma](p,a;[sigma]) this general noncentral Wishart distribution: the real number p is called the shape parameter, the positive definite matrix [sigma] of order k is called the shape parameter and the semi-positive definite matrix a of order k is such that the matrix [omega]=[sigma]a[sigma] is called the noncentrality parameter. This paper considers three problems: the derivation of an explicit formula for the expectation of when X~[gamma](p,a,[sigma]) and h1,...,hm are arbitrary symmetric matrices of order k, the estimation of the parameters (a,[sigma]) by a method different from that of Alam and Mitra [K. Alam, A. Mitra, On estimated the scale and noncentrality matrices of a Wishart distribution, Sankhya, Series B 52 (1990) 133-143] and the determination of the set of acceptable p's as already done by Gindikin and Shanbag for the ordinary Wishart distribution [gamma](p,0,[sigma]).

Keywords: primary; 62H10 secondary; 60B11 Noncentral Wishart Noncentrality Natural exponential families (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (10)

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