Extension of ratio-type estimators for sensitive variables under measurement error and non-response via median ranked-set sampling

Estimating the mean of sensitive variables—such as Drug use—is often challenged by non-response and measurement error. To address these issues, we propose a novel two-phase hybrid estimation framework that integrates median ranked-set sampling (MRSS) and simple random sampling without replacement (SRSWOR), leveraging one or two auxiliary variables to improve the estimation accuracy. The key innovation lies in the strategic combination of MRSS and SRSWOR, tailored to the response dynamics of each phase. Under standard regularity conditions, we derive approximate expressions for bias and mean squared error (MSE) using Taylor expansion. The proposed estimators are validated through simulation studies and applied to estimate the average number of cigarettes smoked daily among university students, using time spent with friends as an auxiliary variable. Our analysis reveals that MRSS offers superior performance in the initial sampling phase, particularly when response rates are low, while SRSWOR is advantageous in the second phase if subsampling proportional to the response rate λ is feasible. In scenarios where full response in the second phase is unattainable, MRSS consistently yields lower MSE. Limitations of the proposed approach include reliance on accurate auxiliary information, the assumption of independence between sampling phases, and the requirement of population symmetry for theoretical derivations involving MRSS. The results underscore the practical utility and robustness of the proposed approach in handling sensitive survey data. Subject Classification: 62D05, 62D99