  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 we wish 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 in 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. In this work,
we propose an implementation of balanced random imputation which enables to
fully eliminate the imputation variance. Following the approach in Cardot et
al. (2013), we consider a regularized imputed estimator of a total and of a
distribution function, and we prove that they are consistent under the proposed
imputation method. Some simulation results support our findings.
