A Unified Approach to Improving Equivariant Estimators

Abstract

In the point and interval estimation of the variance of a normal distri- bution with an unknown mean, the best affine equivariant estimators are dominated by Stein's truncated and Brewster and Zidek's smooth proce- dures, which are separately derived. This paper gives a unified approach to this problem by using a simple definite integral and provides a class of improved procedures in both point and interval estimation of powers of the scale parameter of nonnal, lognormal, exponential and Pareto distri- butions. Finally, the same method is applied to the improvement on the James-Stein rule in the simultaneous estimation of a multinormal mean. 1.