A Novel Approach to Population Mean Estimation Using Two Auxiliary Variables Under PPS Sampling

In many real-world situations, the elements of a population exhibit considerable variation in size. For instance, in surveys related to tuberculosis cases, hospitals or clinics may serve vastly different numbers of patients. Similarly, in evaluating the effects of government subsidy programs, the populations of villages can vary significantly. In such contexts, Probability Proportional to Size (PPS) sampling emerges as a more suitable and effective method. This study introduces a new class of estimators aimed at enhancing the estimation of the population mean within the PPS sampling framework. The bias and mean squared error (MSE) of the proposed estimators are obtained using first-order approximations. To assess their efficiency, a simulation study and empirical analysis using real-world data were carried out. The findings demonstrate that the proposed estimators outperform existing methods, as indicated by their lower MSE values and higher percent relative efficiency (PRE).