On the efficient estimation of population mean under simple random sampling: Applications to ideological education and radiation sciences

The tactical use of auxiliary variables has long been considered a foundation of the theory and practice of survey sampling, increasing the accuracy and efficiency of population parameter estimation. Based on this guiding principle, the current research proposes a new type of estimator for efficiently estimating the finite population mean in the context of Simple Random Sampling (SRS). The suggested class stands out by simultaneously using dual auxiliary variables, namely an auxiliary variable and its rank, thus taking advantage of a more information-rich structure to ensure a higher level of estimation accuracy. Close mathematical derivations are made to find closed-form expressions of the bias and Mean Squared Error (MSE) of the proposed estimators to the first-order approximation. The best conditions under which MSE should be minimized are systematically laid down, offering a theoretically well-grounded basis for practical application. Comparisons of analytical efficiency, based on both bias and MSE criteria, clearly show that the suggested class of estimators is always more efficient and robust than its traditional counterparts, which have significantly higher efficiency and robustness across a broad range of sampling situations and population structures. To further support the theoretical results, a detailed Monte Carlo simulation study is performed across a wide range of population structures, sample sizes, and correlation levels between the study and auxiliary variables. Moreover, empirical validations are also conducted on real-world data borrowed from the spheres of ideological education and radiation sciences — the areas where the accurate estimation of the population properties has a far-reaching practical importance. The theoretical and simulation-based results all confirm the hypothesis that the proposed estimators will always perform better than the current classical and advanced competitors and achieve significant improvements in estimation accuracy.