Additive ratio type exponential estimator of finite population mean of sensitive variable using non-sensitive auxiliary information based on optional randomized response model

The appropriate use of auxiliary information in sample surveys increases the efficiency of estimator for parameter of interest. In this paper, we have proposed an exponential type estimator for the population mean of a sensitive study variable based on an optional randomized response model by using the known information on a non-sensitive auxiliary variable. Expressions for the bias and the mean square error (MSE) of the proposed estimator are derived, up to first order of approximation. For this proposed estimator, efficiency comparisons with the existing estimators have been carried out both theoretically and numerically. It has been shown that our proposed estimator perform better than the existing estimators based on the same optional randomized response model even for the small correlation between auxiliary variable and study variable. To support the results obtained, we have also studied the performance of the proposed exponential estimator using simulation technique.