Estimation of Variance Component for one-way Classification with Heteroscedastic Error

For an unbalanced one-way classification under the random effect model where the error variance remains same within each class bttt varies over the classes, the problem of estimation of the variance component due to class effect is considered. A class of estimates including some estimates suggested from intuitive considerations is examined and it is shown that when the class size can assume only a finite number of distinct values, it is possible to set up an estimate which is asymptotically better than all the_ members of the class. Further, in the 1encral case it is shown that given any estimate belonging to a particular class, it is possible to find a corresponding estimate which is asymptotically bettor.