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September, 1989 Asymptotic Analysis of Minimax Strategies in Survey Sampling
Horst Stenger
Ann. Statist. 17(3): 1301-1314 (September, 1989). DOI: 10.1214/aos/1176347270

Abstract

Suppose that real numbers $y_i$ are associated with the units $i = 1, 2, \ldots, N$ of a population $U$ and that the vector $y = (y_1, y_2, \ldots, y_N)$ is known to be an element of the parameter space $\Theta$. The statistician has to select a sample $s \subset U$ of $n$ units and to employ $y_i, i \in s,$ to estimate $\bar{y} = \sum y_i/N.$ We propose to base this decision on an asymptotic version of the minimax principle. The asymptotically minimax principle is applied to three parameter spaces, including the parameter space considered by Scott and Smith and a space discussed by Cheng and Li. It turns out that stratified sampling is asymptotically minimax if the allocation is adapted to the parameter space. In addition we show that the commonly used ratio strategy [i.e., simple random sampling (srs) together with ratio estimation] and the RHC-strategy (see Rao, Hartley and Cochran) are asymptotically minimax with respect to parameter spaces chosen appropriately.

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Horst Stenger. "Asymptotic Analysis of Minimax Strategies in Survey Sampling." Ann. Statist. 17 (3) 1301 - 1314, September, 1989. https://doi.org/10.1214/aos/1176347270

Information

Published: September, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0719.62022
MathSciNet: MR1015152
Digital Object Identifier: 10.1214/aos/1176347270

Subjects:
Primary: 62D05
Secondary: 62C20

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 3 • September, 1989
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