The Influence of Measurement Errors on Generalized Estimator of Population Mean

Abstract

This paper proposed a generalized estimator of population mean in the presence of correlated and uncorrelated measurement errors under simple random strategy.  Some known estimators belong to this class of proposed estimator.  Under the large sample approximation, the properties of the proposed estimator namely bias and mean squared error were obtained. Theoretical comparison was carried out on the members of the proposed class of estimators when measurement errors are correlated and when they are uncorrelated and the necessary conditions under which the proposed estimator at its optimum value is expected to be more efficient than the existing estimators of finite population mean were obtained.  It was observed that correlated and uncorrelated measurement errors inflate the bias and mean squared error of the proposed estimator. The paper concluded that the proposed estimator is more efficient than usual unbiased estimator  and some members of the class of proposed estimator.