Missing Data Analysis: A Kernel-Based Multi-Imputation Approach

Shichao Zhang, Zhi Jin, Xiaofeng Zhu, Jilian Zhang

Abstract: Many missing data analysis techniques are of single-imputation. However, single-imputation cannot provide valid standard errors and confidence intervals, since it ignores the uncertainty implicit in the fact that the imputed values are not the actual values. Filling in each missing value with a set of plausible values is called multi-imputation. In this paper we propose a kernel-based stochastic non-parametric multi-imputation method under MAR (Missing at Random) and MCAR (Missing Completely at Random) missing mechanisms in nonparametric regression settings. Furthermore, we present a kernel-based stochastic semi-parametric multi-imputation method while we have some priori knowledge about the dataset with missing. Our algorithms are designed specifically with the aim of optimizing the confidence-interval and the relative efficiency. The proposed technique is evaluated by experimentations, using simulation data and real data, and the results demonstrate that our method performs much better than the NORM method, and is promising.