Biases and Variances of Survey Estimators Based on Nearest Neighbor Imputation

NEAREST NEIGHBOR IMPUTATION Jiahua Chen1 University of Waterloo Jun Shao2 University of Wisconsin-Madison Abstract Nearest neighbor imputation is one of the hot deck methods used to compensate for nonresponse in sample surveys. Although it has a long history of application, theoretical properties of the nearest neighbor imputation method are unknown prior to the current paper. We show that under some conditions, the nearest neighbor imputation method provides asymptotically unbiased and consistent estimators of functions of population means (or totals), population distributions, and population quantiles. We also derive the asymptotic variances for estimators based on nearest neighbor imputation and consistent estimators of these asymptotic variances. Some simulation results show that the estimators based on nearest neighbor imputation and the proposed variance estimators have good performances.