An invariance property of common statistical tests

✍ Scribed by N. Rao Chaganty; A.K. Vaish

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 701 KB
• Volume: 264
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)00032-3

✦ Synopsis

Let A be a symmetric matrix and B be a nonnegative definite (nnd) matrix. We obtain a characterization of the class of nnd solutions ~ for the matrix equation A~A = 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 problems in linear algebra.