Median Estimation with Quantile Transformations: Applications to Stratified Two-Phase Sampling.

Most traditional estimators assume normality and remain sensitive to extreme observations, which limits their usefulness in practical applications. To improve accuracy, we introduce quintile-based median estimators using transformation methods in a stratified two-phase sampling technique. The design allows for efficient use of auxiliary data and enhances robustness across heterogeneous strata. Stratified sampling further reduces variability by ensuring representation from all subgroups within the population. Bias and mean squared error expressions are obtained through first-order approximations. The efficiency of the proposed estimators is evaluated using the mean squared error (MSE) as the benchmark criterion. The effectiveness of the proposed estimators is examined by conducting simulations under various skewed distributions. To strengthen the conclusions, additional analysis is performed on real population datasets. Simulation and empirical studies confirm the superior performance of the proposed methods. The findings show that the suggested estimators perform well in practical situations involving median estimation as well as achieving higher precision and effectiveness than existing estimators.