MINQUE and ANOVA Estimator for One-way Classification - a Risk Comparison

For the one-way classification in unbalanced case MINQUEstimator for components of variance are given in a more explicit form than it is done in the paper from C. R. RAO (1971). By means of the risk functions we compare MINQUE and ANOVA estimator. For given n_j-patterns angular ranges in the positive quadrant are given where MINQUE is better than ANOVA estimator. A special n_j-pattern and one parameter δ₀ is found for which MINQUE is uniformly better than ANOVA. Limit values are given for MINQUE for δ₀ = ∞ and δ₀ = 0 and their relations to the ANOVA estimator are considered. The coincidence between MINQUE and ANOVA for balanced case is verified. Extensive numerical studies for real data are carried out which stimulated the search for a fixpoint δ as a point for which the distance to the initial parameter δ₀ is as small as possible.