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.
Publié le : 1981-09-14
Classification:
Finite population,
simple random sampling,
minimax estimator,
means,
labels,
stratified sampling,
sample design,
62D05,
62G05
@article{1176345592,
author = {Bickel, P. J. and Lehmann, E. L.},
title = {A Minimax Property of the Sample Mean in Finite Populations},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 1119-1122},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345592}
}
Bickel, P. J.; Lehmann, E. L. A Minimax Property of the Sample Mean in Finite Populations. Ann. Statist., Tome 9 (1981) no. 1, pp. 1119-1122. http://gdmltest.u-ga.fr/item/1176345592/