Kernel-based multi-imputation for missing data

Abstract

Missing or incomplete data is a very important problem in many fields of research. Such as in active media technology, opinion polls, market research surveys, mail enquiries, medical studies, and other scientific experiments. Missing data imputation is a challenging issue in machine learning and data mining (Zhang et al. 2004; Batista & Monard 2003). Many missing data analysis techniques are of single-imputation which missing values are filled in by a plausible estimate such as the mean or median for that variable on other participants. 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. Recently, much research on missing data analysis has focused on multi-imputation techniques for addressing the issues in single-imputation (Faris et al. 2002; Little et al. 1987; Schaffer 2002; Taylor et al. 2002; Zhang 2004). Little et al. (1987) proposed a multiple imputation procedure to replace each missing value with a set of plausible values that represent the uncertainty about the right value to impute. The multiple-imputed-data sets are then analyzed using a standard procedure for complete data and combining the results from these analyses. In this paper, a kernel-based nonparametric multiple-imputation (KBNM) is proposed under MAR (missing Y mainly depends on X) and MCAR (MCAR is when the probability of missing a value is the same for all variables). The rest of this paper is organized as follows. Our kernel-based multiple imputation method is described in Section 2. Section 3 presents a series of experimental results on simulation models and a real-world dataset (from UeI) to compare the performances between our KBNM approach and the NORM. Conclusions are given in Section 4.