Predictive mean matching imputation in survey sampling

TL;DR

This paper investigates the asymptotic properties of predictive mean matching for survey data, proposing a new bootstrap variance estimation method that remains valid despite the estimator's nonsmooth nature.

Contribution

It introduces an asymptotically valid replication variance estimation approach for predictive mean matching, extending to nearest neighbor imputation.

Findings

The new variance estimator is validated through simulations.

Bootstrap inference is shown to be invalid with traditional methods.

Extension to nearest neighbor imputation is discussed.

Abstract

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.