Document Type

Article

Publication Date

1997

DOI

10.1016/s0024-3795(97)00032-3

Publication Title

Linear Algebra and Its Applications

Volume

264

Pages

421-437

Abstract

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 problems in linear algebra. © 1997 Elsevier Science Inc.

Comments

Elsevier open archive. © 1997 Elsevier Science Inc. All rights reserved.

Original Publication Citation

Chaganty, N. R., & Vaish, A. K. (1997). An invariance property of common statistical tests. Linear Algebra and Its Applications, 264, 421-437. doi:10.1016/s0024-3795(97)00032-3

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