The Annals of Statistics

Moments of minors of Wishart matrices

Mathias Drton, Hélène Massam, and Ingram Olkin

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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.

Article information

Ann. Statist., Volume 36, Number 5 (2008), 2261-2283.

First available in Project Euclid: 13 October 2008

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Zentralblatt MATH identifier

Primary: 60E05: Distributions: general theory 62H10: Distribution of statistics

Compound matrix graphical models multivariate analysis random determinant random matrix tetrad


Drton, Mathias; Massam, Hélène; Olkin, Ingram. Moments of minors of Wishart matrices. Ann. Statist. 36 (2008), no. 5, 2261--2283. doi:10.1214/07-AOS522.

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