Rao-Blackwell versions of the Horvitz-Thompson and Hansen-Hurwitz in adaptive cluster sampling

摘要: Thompson (1990) introduced the adaptive cluster sampling design and developed two unbiased estimators, modified Horvitz-Thompson (HT) Hansen-Hurwitz (HH) for this noticed that these estimators are not a function of minimal sufficient statistics. He applied Rao-Blackwell theorem to improve them. Despite having smaller variances, latter have received attention because suitable method or algorithm computing them was available. In paper we obtain closed forms versions which can easily be computed. We also show variance reduction HH estimator is greater than HT using versions. When condition extra samples \(y > 0\), one expect some improvement in but estimator. Two examples given.