The Superiorities of Bayes Estimation for Variance Components in Random Effects Model

The Bayes estimators of variance components are derived under weighted square loss function for the balanced one-way classification random effects model with the assumption that variance component has the conjugate prior distribution. The superiorities of the Bayes estimators for variance components to traditional ANOVA estimators are studied in terms of the mean square error (MSE) criterion. Finally, a remark for main results is given.