On estimating the common mean of several normal populations under the pitman closeness criterion

Abstract

For the problem of estimating the common mean of k normal populations, the performance of the Graybill-Deal estimator is comparedwith each of the A; sample means using the criterion of Pitman closeness. It is shown that for the Graybill-Deal estimator to dominate any of the sample means it is necessary and sufficient that Ni, the size of the sample from population i, is ≥ 5 for all i when k = 2; and it is sufficient that for all i when k > 2, where . This is a generalization of the result obtained by Kubokawa (1989).