Ratio estimation of the mean of a sensitive variable in the presence of auxiliary information

We propose a ratio estimator for the mean of sensitive variable utilizing information from a nonsensitive auxiliary variable. Expressions for the Bias and MSE of the proposed estimator (correct up to first and second order approximations) are derived. We show that the proposed estimator does better than the ordinary RRT mean estimator that does not utilize the auxiliary information. We also show that there is hardly any difference in the first order and second order approximations for MSE even for small sample sizes. We also generalize the proposed estimator to the case of transformed ratio estimators but these transformations do not result in any significant reduction in MSE. An extensive simulation study is presented to evaluate the performance of the proposed estimator. The procedure is also applied to some financial data (purchase orders (sensitive variable) and gross turn-over (non-sensitive variable)) in 2009 for 5090 companies in Portugal from a survey on Information and Communication Technologies (ICT) usage.