On disguised inverted Wishart distribution
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- by A. K. Gupta and S. Ofori-Nyarko PDF
- Proc. Amer. Math. Soc. 123 (1995), 2557-2562 Request permission
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
- Walter L. Deemer and Ingram Olkin, The Jacobians of certain matrix transformations useful in multivariate analysis, Biometrika 38 (1951), 345–367. MR 47300, DOI 10.1093/biomet/38.3-4.345 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.
- 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 287640, DOI 10.1111/j.2517-6161.1971.tb00867.x
Additional Information
- © Copyright 1995 American Mathematical Society
- 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