ANOVA estimators under imbalance in the one-way random model

The ANOVA estimators of the variance components are studied for the one-way random model with normally distributed effects. The study is focused on the effect of sample-size imbalance on the variance of the estimator for the between-group variance component. Lower and upper bounds for the variance of the estimator are found in terms of the sum of squares of the sample sizes. These bounds encase all possible experimental designs. The effect of imbalance is illustrated by examples. Comparisons are made with the estimators based on restricted maximum likelihood.