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.

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.

In this article, we propose an exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling. The properties of the proposed estimator are obtained and comparison is made with some of the existing estimators. The proposed estimator is found to perform better than the usual mean, ratio, exponential ratio, traditional regression and Pandy ( 1980 Pandy , G. S. ( 1980 ). Product-cum-power estimators . Cal. Statist. Assoc. Bull. 29 : 103 – 108 . [Google Scholar] ) estimators in simple and stratified random sampling. We use six data sets for simple random sampling case and two data sets for stratified random sampling case to compare the performances of all of the estimators considered here.

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.