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October 2008 Moments of minors of Wishart matrices
Mathias Drton, Hélène Massam, Ingram Olkin
Ann. Statist. 36(5): 2261-2283 (October 2008). DOI: 10.1214/07-AOS522


For a random matrix following a Wishart distribution, we derive formulas for the expectation and the covariance matrix of compound matrices. The compound matrix of order m is populated by all m×m-minors of the Wishart matrix. Our results yield first and second moments of the minors of the sample covariance matrix for multivariate normal observations. This work is motivated by the fact that such minors arise in the expression of constraints on the covariance matrix in many classical multivariate problems.


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Mathias Drton. Hélène Massam. Ingram Olkin. "Moments of minors of Wishart matrices." Ann. Statist. 36 (5) 2261 - 2283, October 2008.


Published: October 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1152.62343
MathSciNet: MR2458187
Digital Object Identifier: 10.1214/07-AOS522

Primary: 60E05 , 62H10

Keywords: Compound matrix , graphical models , Multivariate analysis , random determinant , Random matrix , tetrad

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 5 • October 2008
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