Enhanced Estimation Methods Using Auxiliary Information for Rare and Clustered Populations

This research proposes two new estimators which use auxiliary information to derive estimates of population means in cases where populations are considered rare and clustered in line with the General Inverse Adaptive Cluster Sampling (GIACS) framework. A ratio-type estimator is the first to be proposed, while a correlation-type estimator is the second. In this study, theoretical analyses were conducted to derive explicit first-order approximations of the bias and mean squared error for each estimator. The results show that, although the estimators are biased in finite samples, the bias decreases as the sample size increases and converges to zero, implying that the estimators are asymptotically unbiased. Simulation data with symmetric distributions were generated to evaluate their performance. The findings showed that the GIACS estimators using auxiliary information are more efficient than those without. When comparing the performance of estimators that use auxiliary information, it was found that the two proposed estimators, the ratio-type and correlation-type estimators, offered superior efficiency when compared to regression-type estimators. These results confirm that applying auxiliary information can significantly improve the accuracy of estimations within the GIACS framework, making the proposed estimators highly suitable for practical applications involving rare and clustered population.