A Refined Regression Estimator for General Inverse Adaptive Cluster Sampling

Adaptive cluster sampling (ACS) is a sampling technique commonly used for rare populations that exhibit spatial clustering. However, the initially selected sample units may not always satisfy the specified inclusion condition. To address these limitations, general inverse sampling has been incorporated into ACS, in which the initial units are sequentially selected, and a termination criterion is applied to control the number of rare elements drawn from the population. The objective of this study is to develop an estimator of the population mean that incorporates auxiliary information within the framework of general inverse adaptive cluster sampling (GI-ACS). The proposed estimator is constructed based on a regression-type estimator and analytically examined. A simulation study was conducted to validate the theoretical findings. Three scenarios were considered, representing low, moderate, and high correlations between the variable of interest and the auxiliary variable. The simulation results indicate that the proposed estimator achieves lower variance than the GI-ACS estimator that does not utilize auxiliary information across all examined correlation scenarios. Therefore, the proposed estimator is more efficient and preferable when auxiliary variables are available.