Improved estimation of population mean in simple random sampling using information on auxiliary attribute

Abstract

This paper addresses the problem of estimating the population mean with known population proportion of an auxiliary variable. A class of estimators is defined which includes the estimators recently proposed by Shabbir and Gupta (2007) [10] and Abd-Elfattah et al. (2010) [1]. The usual unbiased estimator and Naik and Gupta (1996) [15] estimator are also the member of the proposed class of the estimators. The bias and mean square error (MSE) expressions of the proposed class are obtained up to first order of approximation. Asymptotically optimum estimator (AOE) in the class of estimators is identified alongwith its mean square error formula. The correct MSE and minimum MSE expressions of Shabbir and Gupta (2007) [10] estimator are also given. It has been shown that the proposed class of estimators is more efficient than the usual unbiased estimator, usual linear regression estimator and estimators/classes of estimators due to Naik and Gupta (1996) [15], Jhajj et al. (2008) [9], Shabbir and Gupta (2007) [10] estimator, Singh et al. (2008) [13] and Abd-Elfattah et al. (2010) [1]. The double sampling version of the proposed class of estimators is proposed alongwith its properties. Numerical illustrations are given in support of the present study.