Doubly robust imputation procedures for finite population means in the presence of a large number of zeros

Abstract

AbstractSingle imputation is often used in surveys to compensate for item nonresponse. In some cases, the variable requiring imputation contains a large amount of zeros. This is especially frequent in business surveys that collect economic variables. Motivated by a mixture regression model, we propose three imputation procedures and study their properties in terms of bias and variance. We show that these procedures are doubly robust, leading to consistent estimators of the finite population mean if either the imputation model or the nonresponse model is well specified. For the proposed procedures, we consider a jackknife variance estimator, which is consistent for the true variance, provided the overall sampling fraction is negligible. Finally, the results of a simulation study comparing the performance of point and variance estimators in terms of relative bias and mean square error are presented. The Canadian Journal of Statistics 42: 650–669; 2014 © 2014 Statistical Society of Canada