A Minimax Property of The Sample Mean in Finite Populations
Peter J. Bickel, Erich L. Lehmann · 2011
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 τ 2 . Aggarwal also stated, but did not successfully prove, that the sample mean minimizes the maximum expected squared error over the populations satisfying τ 2 ≤ 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.