Comparison of Two Ratio Estimators Using Auxiliary Information

Abstract

This study is conducted to compare two ratio estimators that use auxiliary information. The estimators are Olkin average ratio estimator and Kadilar-Cingi estimator. Efficiencies of the estimators are investigated theoretically and using data from Federal Inland Revenue Service Revenue House Store. The result shows Kadilar - Cingi estimator is more efficient than Olkin estimator. The estimation of the population mean is a persistent issue in sampling practice and many efforts have been made to improve the precision of the estimates. The literature on survey sampling describes a great variety of techniques for using auxiliary information by means of ratio, product and regression methods. Particularly, in the presence of multi-auxiliary variables, a wide variety of estimators have been discussed, following different ideas, and linking together ratio, product or regression estimators, each one exploiting the variables one at a time. Olkin (1958) was the first author to deal with the problem of estimating the mean of a survey variable when auxiliary variables are made available. He suggested the use of information on more than one supplementary characteristic, positively correlated with the study variable, considering a linear combination of ratio estimators based on each auxiliary variable separately. The coefficients of the linear combination were determined so as to minimize the variance of the estimator. Analogously to Olkin, Singh (1967) gave a multivariate expression of Murthy (1964) product estimator, while Raj (1965) suggested a method for using multi-auxiliary variables through a linear combination of single difference estimators. Moreover, Singh (1967) considered the extension of the ratio-cum-product estimators to multi-supplementary variables, while Rao and Mudholkar (1967) proposed a multivariate estimator based on a weighted sum of single ratio and product estimators. John (1969) suggested two alternative multivariate generalizations of ratio and product estimators