Rita Sousa

Recently, Koyuncu et al. ( 2013 Koyuncu, N. , Gupta, S. , Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation [PubMed], [Web of Science ®] [Google Scholar] ) proposed an exponential type estimator to improve the efficiency of mean estimator based on randomized response technique. In this article, we propose an improved exponential type estimator which is more efficient than the Koyuncu et al. ( 2013 Koyuncu, N. , Gupta, S. , Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation [PubMed], [Web of Science ®] [Google Scholar] ) estimator, which in turn was shown to be more efficient than the usual mean estimator, ratio estimator, regression estimator, and the Gupta et al. ( 2012 Gupta, S. , Shabbir, J. , Sousa, R. , Corte-Real, P. (2012). Regression estimation of the mean of a sensitive variable in the presence of auxiliary information. Communications in Statistics – Theory and Methods 41:2394–2404. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ) estimator. Under simple random sampling without replacement (SRSWOR) scheme, bias and mean square error expressions for the proposed estimator are obtained up to first order of approximation and comparisons are made with the Koyuncu et al. ( 2013 Koyuncu, N. , Gupta, S. , Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation [PubMed], [Web of Science ®] [Google Scholar] ) estimator. A simulation study is used to observe the performances of these two estimators. Theoretical findings are also supported by a numerical example with real data. We also show how to, extend the proposed estimator to the case when more than one auxiliary variable is available.

Sousa et al. (2010) and Gupta et al. (2012) have recently introduced ratio and regression estimators for the mean of a sensitive variable which perform better than the ordinary mean estimator based on a Randomized Response Technique (RRT). In the present study we extend these estimators to the stratified sampling setting. The performance of the proposed estimators is compared to the exiting estimators both theoretically and through a simulation study. We also apply the proposed estimators to some real data.

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.