An identity for the Wishart distribution with applications

L. R. Haff

Journal of Multivariate Analysis, 1979, vol. 9, issue 4, 531-544

Abstract: Let Sp-p have a Wishart distribution with unknown matrix [Sigma] and k degrees of freedom. For a matrix T(S) and a scalar h(S), an identity is obtained for E[summation operator]tr[h(S)T[summation operator]-1]. Two applications are given. The first provides product moments and related formulae for the Wishart distribution. Higher moments involving S can be generated recursively. The second application concerns good estimators of [summation operator] and [summation operator]-1. In particular, identities for several risk functions are obtained, and estimators of [summation operator] ([summation operator]-1) are described which dominate aS(bS-1), a

Keywords: Wishart; and; inverted; moments; estimation; of; covariance; matrix; and; its; inverse; Stoke's; theorem; general; identities; for; the; risk; function (search for similar items in EconPapers)
Date: 1979
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Citations: View citations in EconPapers (49)

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