Conditions for Wishartness and Independence of Second Degree Polynomials in a Normal Vector

DOI10.1214/aoms/1177704467zbMath0108.32405OpenAlexW2080707717MaRDI QIDQ3844748

C. C. Khatri

Publication date: 1962

Published in: The Annals of Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoms/1177704467

zbMATH Keywords

statistics

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Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures ⋮ On the Distribution of Matrix Quadratic Forms ⋮ On randomization in multivariate analysis of variance ⋮ Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix ⋮ The covariance matrix of a general symmetric second degree matrix polynomial under normality assumptions ⋮ The necessary and sufficient conditions for dependent quadratic forms to be distributed as multivariate gamma ⋮ Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms ⋮ Multivariate versions of Cochran's theorems ⋮ Nonnegative definite solutions to matrix equations with applications to multivariate test statis\-tics ⋮ Wishartness and independence of matrix quadratic forms in a normal random matrix ⋮ On the independence between two generalized second degree polynomial statistics and their covariance ⋮ A necessary condition for a quadratic form to have a chi-squared distribution: an accessible proof

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