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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
DOI: https://doi.org/10.1090/S0002-9939-1995-1249879-2
MathSciNet review: 1249879
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Abstract | References | Similar Articles | Additional Information

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] W. L. Deemer and I. Olkin, The Jacobians of certain matrix transformations useful in multivariate analysis, based on lectures of P. L. Hsu at the University of North Carolina, 1947; Biometrika 38 (1951), 345-367. MR 0047300 (13:855c)
  • [2] A. K. Gupta and S. Ofori-Nyarko, Improved minimax estimators of covariance and precision matrices when additional information is available on some coordinates, Department of Mathematics and Statistics, Bowling Green State University, Technical Report No. 93-11, 1993.
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1249879-2
Keywords: Minimax estimation, risk, Jacobian, lower triangular matrix, F-distribution
Article copyright: © Copyright 1995 American Mathematical Society

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