A Refined Regression Estimator for General Inverse Adaptive Cluster Sampling

Adaptive cluster sampling (ACS) is a sampling method commonly employed when the population is rare and exhibits clustering. However, the initial sample selection may include units that do not satisfy the specified condition. To address this, general inverse sampling is incorporated into ACS, where the initial units are selected sequentially and termination criteria are applied to regulate the number of rare elements drawn from the population. The objective of this study is to develop an estimator of the population mean by utilizing auxiliary information within the framework of general inverse adaptive cluster sampling. The proposed estimator, constructed on the basis of a regression-type estimator, is analytically examined. A simulation study was conducted to validate the theoretical results. In this study, the region of interest was divided into 400 square units (20 rows by 20 columns). The results demonstrate that the proposed estimator, which incorporates auxiliary variables, consistently yields a lower variance than the conventional mean estimator without auxiliary information. This superiority holds across all scenarios considered, specifically when the predetermined number of rare units r ranges from two to ten. Therefore, the proposed estimator is shown to be more efficient than the estimator that does not employ auxiliary information.