Improving Mean Estimation through Structured Sampling: Theoretical and Empirical Advances under Ranked Set Sampling

This study introduces several new classes of estimators for the population mean under the framework of Ranked Set Sampling (RSS). This cost-efficient sampling design enhances estimation precision by incorporating judgmental or auxiliary-based ranking. The proposed estimators leverage information from one or more auxiliary variables, utilizing both conventional (e.g., mean) and non-conventional robust measures (e.g., median, Hodges-Lehmann estimator, mid-range) to improve efficiency and resilience against data contamination. These estimators' development is based on a post-stratified RSS framework, which addresses a significant drawback of current approaches that frequently assume error-free auxiliary data by explicitly accounting for measurement error in auxiliary variables. To ensure maximum precision, optimal conditions for minimum mean squared error (MSE) are established, and analytical expressions for bias and MSE are derived up to the first order of approximation. Using two benchmark datasets the factory output data from Murthy (1967) and the apple production survey from Kadilar and Cingi (2006)—rigorous simulation studies and empirical applications are used to assess the performance of the suggested estimators. Findings show that the suggested classes of estimators continuously perform more efficiently than current approaches, especially when measurement error and non-normality are present. In the majority of configurations, the percentage relative efficiency (PRE) values surpass 200%, indicating significant improvements in accuracy. These results demonstrate how crucial it is to incorporate error-in-variables models and strong auxiliary measures into RSS-based estimation, providing a more accurate and practical method for estimating population means in real-world survey scenarios where data errors are unavoidable.