Rao-Blackwell versions of the Horvitz-Thompson and Hansen-Hurwitz in adaptive cluster sampling |
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Authors: | Mohammad Salehi M. |
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Affiliation: | (1) School of Mathematics, Isfahan University of Technology, Isfahan, I.R. of Iran |
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Abstract: | Thompson (1990) introduced the adaptive cluster sampling design and developed two unbiased estimators, the modified Horvitz-Thompson (HT) and Hansen-Hurwitz (HH) estimators, for this sampling design and noticed that these estimators are not a function of the minimal sufficient statistics. He applied the Rao-Blackwell theorem to improve them. Despite having smaller variances, these latter estimators have not received attention because a suitable method or algorithm for computing them was not available. In this paper we obtain closed forms of the Rao-Blackwell versions which can easily be computed. We also show that the variance reduction for the HH estimator is greater than that for the HT estimator using Rao-Blackwell versions. When the condition for extra samples is , one can expect some Rao-Blackwell improvement in the HH estimator but not in the HT estimator. Two examples are given. |
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Keywords: | adaptive sampling clustered population Rao-Blackwell theorem. |
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