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On disguised inverted Wishart distribution

Authors: A. K. Gupta and S. Ofori-Nyarko
Journal: Proc. Amer. Math. Soc. 123 (1995), 2557-2562
MSC: Primary 62H10
MathSciNet review: 1249879
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Abstract: Let $ A \sim {W_p}(n,\Sigma )$ and $ A = ZZ'$ where Z is a lower triangular matrix with positive diagonal elements. Further, let $ B = {A^{ - 1}} = W'W$ have inverted Wishart distribution so that $ W = {Z^{ - 1}}$. In this paper we derive the distribution of $ M = W\Sigma W'$. It is also shown that $ \frac{{n - p + 1}}{{np}}T'MT \sim {F_{p,n - p + 1}}$ where $ T \sim {N_p}(0,{I_p})$ is independent of M.

References [Enhancements On Off] (What's this?)

  • [1] Walter L. Deemer and Ingram Olkin, The Jacobians of certain matrix transformations useful in multivariate analysis, Biometrika 38 (1951), 345–367. Based on lectures of P. L. Hsu at the University of North Carolina, 1947. MR 0047300
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  • [3] W. Y. Tan and Irwin Guttman, A disguised Wishart variable and a related theorem, J. Roy. Statist. Soc. Ser. B 33 (1971), 147–152. MR 0287640

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Keywords: Minimax estimation, risk, Jacobian, lower triangular matrix, F-distribution
Article copyright: © Copyright 1995 American Mathematical Society

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