Nearest neighbor imputation for general parameter estimation in survey sampling

TL;DR

This paper investigates the asymptotic properties of nearest neighbor imputation for estimating various population parameters in survey sampling and proposes a valid replication variance estimation method.

Contribution

It introduces a new asymptotic analysis for nearest neighbor imputation and develops a valid replication variance estimator for complex survey parameters.

Findings

Proposed a valid replication variance estimation method.

Confirmed through simulation that the new variance estimator is accurate.

Analyzed asymptotic properties of the imputation estimator.

Abstract

Nearest neighbor imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the nearest neighbor imputation estimator for general population parameters, including population means, proportions and quantiles. For variance estimation, the conventional bootstrap inference for matching estimators with fixed number of 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. A simulation study confirms that the new procedure provides valid variance estimation.