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June, 1983 A Minimax Approach to Sample Surveys
Ching-Shui Cheng, Ker-Chau Li
Ann. Statist. 11(2): 552-563 (June, 1983). DOI: 10.1214/aos/1176346160

Abstract

Suppose that there is a population of $N$ identifiable units each with two associated values $x_i$ and $y_i$. All $N$ values of $x$ are given but $y_i$ is determined only after the $i$th unit is selected and observed. The objective is to estimate the population total $\sum^N_{i=1} y_i$. It is assumed that $y_i = \theta x_i + \delta_ig(x_i), 1 \leq i \leq N$, where $(\delta_1, \cdots, \delta_N)$ is in some bounded neighborhood of $(0, \cdots 0)$. The Rao-Hartley-Cochran and Hansen-Hurwitz strategies are shown to be approximately minimax under certain models with $g(x) = x^{1/2}$ and with $g(x) = x$, the latter relating to a problem considered by Scott and Smith (1975). These two strategies are then compared with some commonly-used strategies and are found to perform favorably when $g^2(x)/x$ is an increasing function of $x$. The problem of estimating $\theta$ is also considered. Finally, some exact minimax results are obtained for sample size one.

Citation

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Ching-Shui Cheng. Ker-Chau Li. "A Minimax Approach to Sample Surveys." Ann. Statist. 11 (2) 552 - 563, June, 1983. https://doi.org/10.1214/aos/1176346160

Information

Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0524.62015
MathSciNet: MR696066
Digital Object Identifier: 10.1214/aos/1176346160

Subjects:
Primary: 62D05
Secondary: 62C20

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 2 • June, 1983
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