Efficient Estimator of Population Mean of Sensitive Variable in Presence of Scrambled Response Using Auxiliary Information

In this paper, we propose a modified regression exponential estimator of population mean of the sensitive variable for additive model of Randomized Response Technique (RRT) given by Pollack and Bek (1976). The proposed estimator utilizes a sufficiently correlated non-sensitive auxiliary variable to improve estimation accuracy. We derive the expression for bias and mean square error (MSE) of the estimator up to the first order of approximation. Furthermore, an empirical and theoretical study is conducted using artificially generated populations for comparing efficiency of the pro-posed estimator with existing estimators. The results demonstrate that the present relative efficiency of the proposed estimator generally is comparison of the other existing estimators for different values of correlation coefficient.