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 τ2. Aggarwal also stated, but did not successfully prove, that the sample mean minimizes the maximum expected squared error over the populations satisfying τ2 ≤ 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.
Received July, 1980.
Research partially supported by NSF Grant MCS79 03716 and Office of Naval Research Grant N00014 80 C 0163.
AMS 1970 subject classifications. Primary 62D05;secondary.62G05.
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Aggarwal, Om P. (1959). Bayes and minimax procedures in sampling from finite and infinite populations. Ann. Math. Statist. 30 206–218.
Blackwell, David and Girshick, M. A. (1954). Theory of Games and Statistical Decisions. Wiley, New York.
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Bickel, P.J., Lehmann, E.L. (2012). A Minimax Property of The Sample Mean in Finite Populations. In: Rojo, J. (eds) Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1412-4_28
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