The Annals of Statistics

Moments of minors of Wishart matrices

Mathias Drton, Hélène Massam, and Ingram Olkin

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Abstract

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

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

Dates
First available in Project Euclid: 13 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1223908092

Digital Object Identifier
doi:10.1214/07-AOS522

Mathematical Reviews number (MathSciNet)
MR2458187

Zentralblatt MATH identifier
1152.62343

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

Keywords
Compound matrix graphical models multivariate analysis random determinant random matrix tetrad

Citation

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. https://projecteuclid.org/euclid.aos/1223908092


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