We propose a ratio estimator for the mean of sensitive variable utilizing information from a nonsensitiveauxiliary variable. Expressions for the Bias and MSE of the proposed estimator (correct up tofirst and second order approximations) are derived. We show that the proposed estimator does betterthan the ordinary RRT mean estimator that does not utilize the auxiliary information. We also showthat there is hardly any difference in the first order and second order approximations for MSE even forsmall sample sizes. We also generalize the proposed estimator to the case of transformed ratio estimatorsbut these transformations do not result in any significant reduction in MSE. An extensive simulationstudy is presented to evaluate the performance of the proposed estimator. The procedure is alsoapplied to some financial data (purchase orders (sensitive variable) and gross turn-over (non-sensitivevariable)) in 2009 for 5090 companies in Portugal from a survey on Information and CommunicationTechnologies (ICT) usage.
|Journal||Journal of Statistical Theory and Practice|
|Publication status||Published - 1 Jan 2010|