A Minimax Property of The Sample Mean in Finite Populations

Abstract

Consider the problem of estimating the mean of a finite population on the basis of a simple random sample. It was proved by Aggarwal (1954) that the sample mean minimizes the maximum expected squared error divided by the population variance T2. Aggarwal also stated, but did not successfully prove, that the sample mean minimizes the maximum expected squared error over the populations satisfying T2 c M for any fixed positive M. It is the purpose of this paper to give a proof of this second result, and to indicate some generalizations.