Moments of minors of Wishart matrices. (English) Zbl 1152.62343

Drton, Mathias; Massam, Hélène; Olkin, Ingram

Ann. Stat. 36, No. 5, 2261-2283 (2008).

Summary: 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 \(m\times m\)-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.

MSC:

62H10	Multivariate distribution of statistics
15B52	Random matrices (algebraic aspects)
60E05	Probability distributions: general theory

Keywords:

compound matrix; graphical models; multivariate analysis; random determinant; random matrix; tetrad

Software:

TETRAD; SAS

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