OPTIMUM INVARIANT TESTS IN MIXED LINEAR MODELS WITH TWO VARIANCE COMPONENTS

Abstract

In a mixed linear model with two variance components, optimum invariant tests are derived for the significance of a variance component for one-sided and two-sided alternatives. When the alternative is one-sided, a locally best invariant (LBI) test always exists, which is uniformly most powerful invariant (UMPI) under a condition. Under the same condition, a uniformly most powerful invariant unbiased test exists for the two sided alternative and without this condition, a locally best invariant unbiased test can be obtained. The LBI and UMPI character of Wald's variance component test is also investigated. The results are applied to some Anova models, a model from genetics and the nearest neighbor correlation model.