Jackknife Variance Estimation for Nearest-Neighbor Imputation

Abstract

Nearest-neighbor imputation is a popular hot deck imputation method used to compensate for nonresponse in sample surveys. Although this method has a long history of application, the problem of variance estimation after nearest-neighbor imputation has not been fully investigated. Because nearest-neighbor imputation is a nonparametric method, a nonparametric variance estimation technique, such as the jackknife, is desired. We show that the naive jackknife that treats imputed values as observed data produces serious underestimation. We also show that Rao and Shao's adjusted jackknife, or the jackknife with each pseudoreplicate reimputed, which produces asymptotically unbiased and consistent jackknife variance estimators for other imputation methods (such as mean imputation, random hot deck imputation, and ratio or regression imputation), produces serious overestimation in the case of nearest-neighbor imputation. Two partially reimputed and a partially adjusted jackknife variance estimators are proposed and shown to be asymptotically unbiased and consistent. Some empirical results are provided to examine finite-sample properties of these jackknife variance estimators.