  Predictive mean matching imputation is popular for handling item nonresponse
in survey sampling. In this article, we study the asymptotic properties of the
predictive mean matching estimator of the population mean. For variance
estimation, the conventional bootstrap inference for matching estimators with
fixed matches has been shown to be invalid due to the nonsmoothness nature of
the matching estimator. We propose asymptotically valid replication variance
estimation. The key strategy is to construct replicates of the estimator
directly based on linear terms, instead of individual records of variables.
Extension to nearest neighbor imputation is also discussed. A simulation study
confirms that the new procedure provides valid variance estimation.
