Nonparametric Variance Estimation for Nearest Neighbor Imputation

Nearest neighbor imputation is a popular nonparametric hot deck imputation method used to compensate for nonresponse in sample surveys. Although the nearest neighbor imputation method has a long history of application, no asymptotically consistent nonparametric variance estimator for a survey estimator (such as the sample mean) based on data with nonrespondents imputed by nearest neighbor was available until the proposal of the adjusted jackknife variance estimator by Chen and Shao (2001). However, the adjusted jackknife method involves a somewhat artificial adjustment and is computationally complex because every jackknife pseudo-replicate has to be adjusted. We propose a consistent nonparametric variance estimator that is much easier to compute than the jackknife estimator. Some simulation results are provided to examine finite sample properties of the proposed variance estimator.