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An Invariance Property Of Common Statistical Tests, N. Rao Chaganty, A. K. Vaish
An Invariance Property Of Common Statistical Tests, N. Rao Chaganty, A. K. Vaish
Mathematics & Statistics Faculty Publications
Let A be a symmetric matrix and B be a nonnegative definite (nnd) matrix. We obtain a characterization of the class of nnd solutions Σ for the matrix equation AΣA = B. We then use the characterization to obtain all possible covariance structures under which the distributions of many common test statistics remain invariant, that is, the distributions remain the same except for a scale factor. Applications include a complete characterization of covariance structures such that the chisquaredness and independence of quadratic forms in ANOVA problems is preserved. The basic matrix theoretic theorem itself is useful in other characterizing …