Robust Imputation Methods in the Presence of Influential Units in Surveys

Abstract

Item nonresponse is typically addressed by using single imputation techniques. When influential units are present in a sample, the classical imputed estimator of a population total is approximately unbiased provided that the first moment of the imputation model is correctly specified but may be very unstable. Thus, it is desirable to develop robust imputation methods that produce biased but more stable imputed estimators, that is an estimator whose mean square error is smaller than that of the corresponding non-robust imputed estimator. To achieve this, we propose using robust regression based on the Huber function with an adaptive tuning constant. In this thesis, we study three robust imputed estimators in the presence of influential units. We conduct a simulation study to compare the empirical performance of the proposed methods in terms of bias and relative efficiency for a wide range of distributions. Finally, we study the problem of mean square error estimation using both first-order Taylor procedures and bootstrap.