On admissible invariant estimators of variance components which dominate unbiased invariant estimators

A characterization of admissible invariant quadratic estimators for linear combinations of variance components for mixed linear models is established.This allows us to construct for the balanced random, one–way ANOVA model, as well as for some other mixed linear models, admissible estimators which are also better than the best unbiased estimator with respect to the matrix risk function. Admissible estimators better than the best unbiased estimator may be used to construt admissible estimators which dominate the unbiased estimators for any parametric function of the variance components.