Assessment of variance components in elliptical linear mixed models

Abstract

The aim of this article is to discuss the problem of testing variance components in elliptical linear mixed models. The elliptical class includes all symmetrical continuous distributions, such as normal, Student-t, Pearson VII, power exponential, logistic I, logistic II, and so on. An approach for elliptical linear mixed models is proposed. The estimation procedure for the fixed parameters, variance components and random effects is also presented and a score-type test for one-sided alternatives to assess the variance components is investigated. Finally, two illustrative examples are given in which normal linear mixed models are compared with elliptical linear mixed models with heavy-tailed error distributions.