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Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms |
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| Authors: | Yongge Tian George P. H. Styan |
| Affiliation: | a School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, Chinab Department of Mathematics and Statistics, McGill University, Canada H3A 2K6 |
| 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 |
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