Kadilar and Cingi [Ratio estimators in simple random sampling, Appl. Math. Comput. 151 (3) (2004), pp. 893–902] introduced some ratio-type estimators of finite population mean under simple random sampling. Recently, Kadilar and Cingi [New ratio estimators using correlation coefficient, Interstat 4 (2006), pp. 1–11] have suggested another form of ratio-type estimators by modifying the estimator developed by Singh and Tailor [Use of known correlation coefficient in estimating the finite population mean, Stat. Transit. 6 (2003), pp. 655–560]. Kadilar and Cingi [Improvement in estimating the population mean in simple random sampling, Appl. Math. Lett. 19 (1) (2006), pp. 75–79] have suggested yet another class of ratio-type estimators by taking a weighted average of the two known classes of estimators referenced above. In this article, we propose an alternative form of ratio-type estimators which are better than the competing ratio, regression, and other ratio-type estimators considered here. The results are also supported by the analysis of three real data sets that were considered by Kadilar and Cingi.

Model efficiency and respondent privacy are two important considerations while comparing two randomized response technique (RRT) models. Either the model efficiency level is kept fixed and the model offering greater privacy is preferred, or the privacy level is kept fixed and we prefer the model with better efficiency. In our current work, we propose a unified measure of model quality for a quantitative RRT model and compare several competing models with respect to this measure.

Sousa et al. ( 2010 Sousa , R. , Shabbir , J. , Real , P. C. , Gupta , S. ( 2010 ). Ratio estimation of the mean of a sensitive variable in the presence of auxiliary information . J. Statist. Theor. Prac. 4 ( 3 ): 495 – 507 . [Taylor & Francis Online] [Google Scholar] ) introduced a ratio estimator for the mean of a sensitive variable and showed that this estimator performs better than the ordinary mean estimator based on a randomized response technique (RRT). In this article, we introduce a regression estimator that performs better than the ratio estimator even for modest correlation between the primary and the auxiliary variables. The underlying assumption is that the primary variable is sensitive in nature but a non sensitive auxiliary variable exists that is positively correlated with the primary variable. Expressions for the Bias and MSE (Mean Square Error) are derived based on the first order of approximation. It is shown that the proposed regression estimator performs better than the ratio estimator and the ordinary RRT mean estimator (that does not utilize the auxiliary information). We also consider a generalized regression-cum-ratio estimator that has even smaller MSE. An extensive simulation study is presented to evaluate the performances of the proposed estimators in relation to other estimators in the study. The procedure is also applied to some financial data: purchase orders (a sensitive variable) and gross turnover (a non sensitive variable) in 2009 for a population of 5,336 companies in Portugal from a survey on Information and Communication Technologies (ICT) usage.

Kadilar and Cingi ( 2006 Kadilar , C. , Cingi , H. ( 2006 ). Improvement in variance estimation using auxiliary information . Hacett. J. Math. Statist. 35 ( 1 ): 111 – 115 . [Google Scholar] ) have introduced an estimator for the population variance using an auxiliary variable in simple random sampling. We propose a new ratio-type exponential estimator for population variance which is always more efficient than usual ratio and regression estimators suggested by Isaki ( 1983 Isaki , C. T. ( 1983 ). Variance estimation using auxiliary information . J. Amer. Statist. Assoc. 78 : 117 – 123 . [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ) and by Kadilar and Cingi ( 2006 Kadilar , C. , Cingi , H. ( 2006 ). Improvement in variance estimation using auxiliary information . Hacett. J. Math. Statist. 35 ( 1 ): 111 – 115 . [Google Scholar] ). Efficiency comparison is carried out both mathematically and numerically.