An Efficient Class of Estimators for the Population Mean Using Auxiliary Information

Abstract

This article addresses the problem of estimating the population mean in the presence of auxiliary information. A class of estimators for population mean is defined. Asymptotic expressions of the bias and mean squared error of the proposed class of estimators were obtained. Asymptotic optimum estimator (AOE) in the proposed class of estimators was identified along with its mean squared error formula. It has been shown that the proposed class of estimators is more efficient than the usual regression estimator and Khoshnevisan et al. (2007 Khoshnevisan , M. , Singh , R. , Chauhan , P. , Sawan , N. , Smarandache , F. ( 2007 ). A general family of estimators for estimating population mean using known value of some population parameter(s) . Far East J. Theor. Statist. 22 : 181 – 191 . [Google Scholar]), Singh et al. (2007 Singh , R. , Chouhan , P. , Sawan , N. , Smarandache , F. ( 2007 ). Rato-Product Type Exponential Estimator for Estimating Finite Population Mean Using Information on Auxiliary Attribute. Auxiliary Information and a Priori Values in Construction of Improved Estimators . Gallup , NM : Renaissance High Press, pp. 18–32 . [Google Scholar]), and Koyuncu and Kadilar (2009a Koyuncu , N. , Kadilar , C. ( 2009a ). Efficient estimators for the population mean . Hacett. J. Math. Statist. 38 ( 2 ): 217 – 225 .[Web of Science ®] , [Google Scholar]) classes of estimators.