An invariance property of common statistical tests

Autor:	N. Rao Chaganty, A.K. Vaish
Rok vydání:	1997
Předmět:	Discrete mathematics Numerical Analysis Algebra and Number Theory Invariant (physics) Covariance Sylvester's law of inertia Matrix (mathematics) Linear algebra Symmetric matrix Discrete Mathematics and Combinatorics Nonnegative matrix Geometry and Topology Statistical hypothesis testing Mathematics
Zdroj:	Linear Algebra and its Applications. 264:421-437
ISSN:	0024-3795
DOI:	10.1016/s0024-3795(97)00032-3
Popis:	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 chi-squaredness 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9f473de8432f70c7f25117ac12a901fe Zobrazit plný text záznamu Full Text from ScienceDirect