On the Optimal Search for Efficient Estimators of Population Mean in Simple Random Sampling in the presence of an Auxiliary Variable

Abstract

This study proposes some ratio estimators of the population mean under simple random sampling schemes, in order to tackle the problem of low efficiencies of some existing estimators. An improved exponential ratio estimator of the population mean under simple random sampling scheme and its bias and mean square error have been derived. Further propositions of a generalized form of the exponential ratio estimator of the population mean under simple random sampling scheme has also been made. The Bias and Mean Square Errors of these class of estimators have also been obtained. It is observed that some existing estimators are members of this class of estimators of population mean. Analytical and numerical results indicate that, the Asymptotic Optimal Estimator (AOE) of these proposed estimators of population mean using single auxiliary variable have been found to exhibit greater gains in efficiencies than the classical regression estimators and other existing estimators in simple random sampling scheme.