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March, 1979 A Minimax Approach to Randomization and Estimation in Survey Sampling
H. Stenger
Ann. Statist. 7(2): 395-399 (March, 1979). DOI: 10.1214/aos/1176344622

Abstract

We consider a finite set of units, a population. With each unit is associated a real value (unknown to us) and a label (identifying the unit). Based on the labels we may select a sample, i.e., a subset of the population, to estimate the mean of the real values. In simple random sampling (not necessarily of fixed size) the selection probabilities of all samples are not affected by a permutation of the labels. It is assumed that we have to choose both a sampling design and a linearly invariant estimator, i.e., a linear function of the observed values with the property: equality of the observed values implies that the estimate is equal to this common value. Under these conditions we should use simple random sampling together with the sample mean as an estimator. This follows from the minimax criterion.

Citation

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H. Stenger. "A Minimax Approach to Randomization and Estimation in Survey Sampling." Ann. Statist. 7 (2) 395 - 399, March, 1979. https://doi.org/10.1214/aos/1176344622

Information

Published: March, 1979
First available in Project Euclid: 12 April 2007

zbMATH: 0399.62007
MathSciNet: MR520248
Digital Object Identifier: 10.1214/aos/1176344622

Subjects:
Primary: 65D05
Secondary: 62K05

Keywords: finite populations , modified minimax principle of Wesler , simple random sampling and symmetric estimation , simultaneous application to randomization and estimation

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 2 • March, 1979
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