Improved Ratio Estimators in Adaptive Cluster Sampling

For better inference of the population quantity of interest, ratio estimators are often recommended when certain auxiliary variables are available. Two types of ratio estimators, modified for adaptive cluster sampling via transformed population and initial intersection probability approaches, have been studied in Dryver and Chao (2007). Unfortunately, none of them are a function of a minimal sufficient statistic, and therefore can be improved with Rao-blackwellization procedure. The purpose of this paper is to obtain new ratio estimators that are not only more efficient than the original ratio estimators proposed by Dryver and Chao, but simple to calculate. Additionally, explicit formulas for the approximated variance of these easy-to-compute estimators are derived.