A Class of Ratio and Product Types Estimators of Mean of a Sensitive Variable Using Ranked Set Sampling

In this paper, we introduce a novel ranked set generalized randomized response estimator designed for accurately estimating the mean of sensitive variables while maintaining the privacy of sensitive information. This method incorporates an additive scramble response technique, which effectively addresses the challenge of estimating the mean of such variables. Through a rigorous analysis, we derive expressions for both bias and mean square error (MSE) pertaining to the proposed estimator and its constituent estimators, to the first-order of approximation. By identifying specific conditions, we highlight scenarios in which the performance of the suggested estimator surpasses alternatives. To substantiate the effectiveness of our approach, we conduct efficiency comparisons, a comprehensive simulation and real data study. These analyses collectively demonstrate the superior performance of our proposed estimator within the framework of ranked set sampling (RSS) for sensitive variables.