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Biometrika 1984 71(1):171-175; doi:10.1093/biomet/71.1.171
© 1984 by Biometrika Trust
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On unequal probability sampling: Sufficient conditions for the superiority of sampling without replacement

S. GABLER

Department of Economics and Statistics, University of Mannheim Mannheim, Federal Republic of Germany

A challenging theoretical problem in unequal probability sampling is the question which design, sampling with or without replacement, should be implemented. In this context we compare the Horvitz-Thompson estimator with the Hansen-Hurwitz estimator and derive conditions under which the variance of the Horvitz-Thompson estimator is smaller than the variance of the Hansen-Hurwitz estimator. Examples are given showing the validity of these conditions.

Key Words: Hansen-Hurwitz estimator • Horvitz-Thompaon estimator • Sampling with and without replacement • Stochastic matrix


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