Exact balanced random imputation for sample survey data

Surveys usually suffer from non-response, which decreases the effective sample size. Item non-response is typically handled by means of some form of random imputation if it is of interest to preserve the distribution of the imputed variable. This leads to an increased variability due to the imputation variance, and several approaches have been proposed for reducing this variability. Balanced imputation consists of selecting residuals at random at the imputation stage, in such a way that the imputation variance of the estimated total is eliminated or at least significantly reduced. The proposed implementation of balanced random imputation enables full elimination of the imputation variance. A regularized imputed estimator of a total and of a distribution function is considered, and is proved to be consistent under the proposed imputation method. Some simulation results support the findings.