On some robust imputation methods in presence of correlated measurement errors with a real data application

Abstract

Missing data occurs frequently in sample surveys. Numerous imputation techniques have been proposed to tackle the problem of missing data, and, in fact, limited works are available in the literature to deal with the issue of missingness while the data are ridden with measurement errors (ME). In addition, no work has been done on the robustness to handle the issue of missing data when it is contaminated with correlated measurement errors (CME). This article proposes some robust imputation methods (RIM) to impute the missing data in the presence of CME. The mean square error (MSE) of the proposed RIM is derived from the first-order approximation and examined with the MSE of the conventional imputation methods. The results are theoretically established and explained using a vast simulation study. Two applications of real data sets are presented to illustrate the efficiency and superiority of the suggested estimators relative to some estimators considered in this study.