ROBUST RATIO BASED AND PRODUCT BASED ESTIMATORS FOR POPULATION MEAN USING MEDIAN OF THE AUXILIARY VARIABLE AND MODIFIED MAXIMUM LIKELIHOOD

In this paper, we incorporate robust ratio based estimator as well as product based estimators for population mean, using known median of the auxiliary variable, through modified maximum likelihood. The mean square errors of the proposed estimators have been obtained theoretically. We also provide certain conditions under which the proposed estimators have minimum mean square error compared to other relevant estimators. For the support of the theoretical outcomes, simulation studies have been performed under several super-population models. We also study the robustness properties of the proposed estimators. We show that the modified maximum likelihood estimates (MMLE’s), in estimating finite population mean, results to robust estimates under non-normality or under common data anomalies such as outliers.