Ban Estimators of Variance Components for the Unbalanced One–Way Classification

Abstract

For unbalanced one-way classification under the random model, the weighted least square approach with estimated weights is used on a set of minimal sufficient statistics in the translation invariant class, and a relatively simple estimator for the pair of variance components is obtained. The estimator is shown to be best asymptotically normal when the number of levels increases. The asymptotic distribution of the proposed estimator remains unaltered, even under a super population model.