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April 1996 The Lukacs-Olkin-Rubin characterization of Wishart distributions on symmetric cones
M. Casalis, G. Letac
Ann. Statist. 24(2): 763-786 (April 1996). DOI: 10.1214/aos/1032894464

Abstract

We characterize the Wishart distributions on a symmetric cone C. If $C = (0, +\infty)$, this has been done by Lukacs in 1955. If C is the cone of positive definite symmetric matrices, this has been done by Olkin and Rubin in 1962. We both shorten and extend the Olkin-Rubin proof (sometimes obscure) by using three modern ideas: (i) try to avoid artificial coordinates in differential geometry; (ii) the variance function of a natural exponential family F characterizes F; (iii) symmetric matrices are a particular example of a Euclidean simple Jordan algebra.

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M. Casalis. G. Letac. "The Lukacs-Olkin-Rubin characterization of Wishart distributions on symmetric cones." Ann. Statist. 24 (2) 763 - 786, April 1996. https://doi.org/10.1214/aos/1032894464

Information

Published: April 1996
First available in Project Euclid: 24 September 2002

zbMATH: 0906.62053
MathSciNet: MR1394987
Digital Object Identifier: 10.1214/aos/1032894464

Subjects:
Primary: 62H05
Secondary: 60E10

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 2 • April 1996
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