Optimizing Finite Population Mean Estimation Using Simulation and Empirical Data

Two-phase sampling is an effective sampling approach that is useful in sample surveys when prior auxiliary information is not available. When two variables have an association, the ranks of the auxiliary variable are proportional to the study variable. Therefore, we can use these rankings to improve the accuracy of the estimators. In this article, we estimate the overall mean of the study variable based on extreme values and the ranks of the auxiliary variable. The properties of the proposed estimators with respect to biases and mean squared errors (MSEs) in two-phase sampling are obtained up to first order approximation. We verify the theoretical results and assess the performance of the proposed estimators using three datasets and a simulation study, which show that the proposed estimators outperform other existing estimators in terms of percent relative efficiency (PRE).