Abstract
There are no uniformly best invariant quadratic estimators of the variance components in the random, one-way ANOVA model. In the balanced model the ANOVA estimators are best among unbiased estimators, but are inadmissible among all invariant quadratic estimators. Two classes of admissible invariant quadratic estimators are presented in this paper: unbiased estimators which have minimum average variance over a prior distribution on the variance components and biased estimators which have minimum average mean squared-error.
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