A1097
Title: Closure of noncentral Wishart mixtures and testing random effects in multivariate factorial designs
Authors: Frederic Ouimet - Universite du Quebec a Trois-Rivieres (Canada) [presenting]
Abstract: Consider mixtures of noncentral Wishart distributions where both the mixing and mixed laws share the same degrees of freedom. It is shown that such a mixture remains noncentral Wishart with the same degrees of freedom, a closure property that extends known univariate chi-square results to arbitrary dimension $d \ge 1$ and general scale matrices. Leveraging this fact, exact finite-sample reference distributions are derived for multivariate tests of random effects in balanced two-factor factorial designs with $d$-dimensional normal responses. In particular, the classical eigenvalue-based statistics built from sums of outer products and the pooled error matrix have a matrix-variate beta type II (matrix $F$) distribution under the null, enabling rigorous tests for covariance components without asymptotic approximations. The methodology applies as well when some factors are fixed, and extends readily to models with more than two factors.
