Advanced Technique for Mean Estimation under Random Non-Response using Dual Auxiliary Information with Observed Heterogeneity

This study addresses the issue of random non-response (RNR) in the study data by introducing improved generalized ratio estimators for the heterogeneous population mean. The novelty of the proposed methodology is to optimize the combined ratio estimator using Searls (1964) idea instead of conventional mean for the heterogeneous population. To study the characterization properties of the proposed estimators, mathematical expressions for the bias and mean square error \((MSqE)\) $(MSqE)$ are derived under stratified simple random sampling technique. The optimal performance of the estimators is obtained along with the required constraints, and a comprehensive theoretical comparison between the proposed and adopted estimators is made. The precision of the suggested estimators in comparison to the adopted estimators based on conventional and well-established estimators has been demonstrated by both the empirical analysis on the body fat dataset and the Monte Carlo simulation technique. The results of this study highlight the fact that the suggested estimators outperform all existing traditional and well-established estimators adopted under this scenario.