A Brief Derivation of Necessary and Sufficient Conditions for a Family of Matrix Quadratic Forms to Have Mutually Independent Non-Central Wishart Distributions

Phil D. Young (), Joshua D. Patrick and Dean M. Young
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Phil D. Young: Baylor University
Joshua D. Patrick: One Bear Place #97140, Baylor University
Dean M. Young: One Bear Place #97140, Baylor University

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 18, 478-484

Abstract: Abstract We provide a new, concise derivation of necessary and sufficient conditions for a real matrix-normally distributed matrix X and we characterize the general matrix-normal covariance structure such that, given the symmetric positive-semidefinite matrices Ai, i = 1,2,...,m, the matrix quadratic forms X ′ A i X ${\textbf {X}}^{\prime }{\textbf {A}}_{i}{\textbf {X}}$ are distributed as independent noncentral Wishart matrices.

Keywords: Matrix trace; Kronecker product; chi-square random variable; matrix equations; generalized inverse matrix; Primary 15A09; Secondary 15A52 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13171-021-00260-5

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