Estimation of Finite Population Mean Using Ratio Estimator Based on Known Median of Auxiliary Variable in the Presence of Non-Response

Abstract

The issue of non-response is a common phenomenon in sample surveys. Therefore, there is a need to develop ways of dealing with the challenge whenever it occurs. The current paper first introduces the stratification of the population as a result of the non-response. A theoretical review of the basic non response in sampling is as well explained and derived. The condition that leads to the first non-response estimator as proposed by the Hansen and Hurwitz. The resampling scheme for the non-response adjustment was described. This forms the bases for the new model which proposes a modified ratio estimator of the finite population mean in the presence of non-response when the population median of the auxiliary variable is known. The properties of the proposed estimators are derived and theoretically compared with existing ones. A theoretical efficiency comparison shows that the proposed estimator performs better than the existing ones. Further, the simulated numerical comparison shows that the Bias of the proposed estimator performs better, while its Mean squared error is competitive. Towards, the conclusion of the study we recommend further studies on the band with that balance the impact on the estimator in terms of the variance and the bias. Further, an exponential ratio form of the proposed estimator was recommended to be studied and its properties be examined.