A Novel Robust Transformation Approach to Finite Population Median Estimation Using Monte Carlo Simulation and Empirical Data

This study develops an improved family of estimators for estimating the finite population median within a two-phase sampling method. The proposed estimators, which use transformation techniques to reduce survey costs when full auxiliary information is unavailable, yield more accurate results than traditional methods. These transformations employ robust statistical measures such as Hodges–Lehmann location, Gini mean difference, and Bowley’s skewness, which strengthen resistance against outliers and heavy-tailed distributions. Through the use of these modern tools within the two-phase sampling framework, the proposed estimators achieve greater flexibility and robustness compared to conventional quantile-based approaches. A first-order approximation is employed to derive the bias and mean squared error expressions. The performance of the proposed estimators is examined through simulation experiments across multiple distributional scenarios and validated using real datasets against standard approaches. Findings based on percent relative efficiency confirm that the proposed estimators improve the accuracy and efficiency of median estimation in two-phase sampling, demonstrating superiority over conventional methods across various practical scenarios.