Estimation of Variance Components in Mixed Linear Models

In mixed linear models with two variance components, classes of estimators improving on ANOVA estimators for the variance components and the ratio of variances are constructed on the basis of the invariant statistics. Out of the classes, consistent, improved and positive estimators are singled out. These estimators are shown to be further dominated by utilizing the information contained in the noninvariant statistics. Applications to the unbalanced one-way ANOVA models and to balanced incomplete block designs are given.