Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

Authors: Tian, Yongge¹; Styan, George P. H.²

Source: Linear and Multilinear Algebra, Volume 53, Number 5, September–October 2005 , pp. 387-392(6)

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Abstract:

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.

Keywords: Chi-squared distribution; Idempotent matrix; Kronecker product; Matrix quadratic form; Matrix version of Cochran's theorem; Outer inverse of a matrix; Quadratic forms in normal variables; Rank additivity; Rank equalities; Rank formulas for partitioned matrices; Rank subtractivity; Wishart distribution; AMS Subject Classifications: 15A09; 15A24; 62H10

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03081080500149040

Affiliations: 1: School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China 2: Department of Mathematics and Statistics, McGill University, 805 ouest, rue Sherbrooke Street West, Montréal (Québec), Canada H3A 2K6

Publication date: 2005-09-01