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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?)

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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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