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September, 1981 A Minimax Property of the Sample Mean in Finite Populations
P. J. Bickel, E. L. Lehmann
Ann. Statist. 9(5): 1119-1122 (September, 1981). DOI: 10.1214/aos/1176345592

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 $\tau^2$. Aggarwal also stated, but did not successfully prove, that the sample mean minimizes the maximum expected squared error over the populations satisfying $\tau^2 \leq M$ 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.

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P. J. Bickel. E. L. Lehmann. "A Minimax Property of the Sample Mean in Finite Populations." Ann. Statist. 9 (5) 1119 - 1122, September, 1981. https://doi.org/10.1214/aos/1176345592

Information

Published: September, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0478.62012
MathSciNet: MR628768
Digital Object Identifier: 10.1214/aos/1176345592

Subjects:
Primary: 62D05
Secondary: 62G05

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 5 • September, 1981
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