Ratio estimates in adaptive cluster sampling

In this study, simple and ratio estimators of Horvitz-Thompson and Hansen-Hurwitz are investigated in the literature in order to obtain an estimate of population mean in adaptive cluster sampling. These estimators do not have sufficient statistics. Simple and ratio estimators of the modified Horvitz-Thompson and Hansen-Hurwitz estimators improved by the Rao-Blackwell method have been investigated in order to obtain estimators with minimum sufficient statistics. We calculated mean and variance estimates of the estimators with numerical example. As a result of this study, it is shown numerically that the variance estimates of the ratio estimators improved by Rao-Blackwell method is smaller.