Alternative estimators for the variance of several normal populations

The problem of interest is to estimate the common variance of k (k ≥ 2) normal populations with possibly different means, based on k independent samples from these populations. Improved estimators over the usual estimator under a large class of bowl-shaped loss functions are proposed. These estimators are similar to those of Brewster and Zidek (1974). However, the regions of the parameter space over which these estimators have the most reduction in risk and the magnitude of risk reduction over the usual estimator are different than those of Brewster and Zidek.