Estimation of Population Mean Using Three-Stage Optional RRT Model in the Presence of Measurement Errors under Stratified Two-Phase Sampling

Abstract

In the present study, the problem of estimation of the finite population mean of a sensitive study variable using the three-stage optional Randomized Response Technique (RRT) model under measurement errors is addressed. A generalized class of estimators is proposed using a mixture of auxiliary attribute and variable. Some members of the proposed generalized class of estimators are identified and studied. The bias and mean square error expressions for the proposed estimators are correctly derived up to first order Taylor’s series of approximation. The proposed estimator’s efficiency is investigated theoretically and numerically using both real data and simulated data. From the numerical study, the proposed estimators outperforms other existing estimators of the finite population mean. Furthermore, efficiencies of the proposed estimators of the finite population mean decreases as sensitivity level of the survey question increases.