Efficiency of modified generalized imputation scheme for estimating population mean with known auxiliary information

Different authors for estimating population mean have proposed several Imputation schemes. Recently, some authors have suggested generalized imputation schemes that their estimators are functions of unknown parameters of the study variable. These unknown parameters need to be estimated for the estimators to be applicable and this may require additional resources. This paper considered a class of imputation scheme that is independent of unknown parameter and the point estimator of the suggested scheme for estimating population mean was derived. The properties (bias and MSE) of an efficient estimators presented were derived up to first order approximation and also conditions for which the estimators of the proposed scheme is more efficient than other estimators of the existing schemes considered in the study were also examined. The result of the empirical study revealed that the suggested estimators are more efficient than the existing ones considered in the study.