A Nonparametric Test of Missing Completely at Random for Incomplete Multivariate Data.

Missing data occur in many real world studies. Knowing the type of missing mechanisms is important for adopting appropriate statistical analysis procedure. Many statistical methods assume missing completely at random (MCAR) due to its simplicity. Therefore, it is necessary to test whether this assumption is satisfied before applying those procedures. In the literature, most of the procedures for testing MCAR were developed under normality assumption which is sometimes difficult to justify in practice. In this paper, we propose a nonparametric test of MCAR for incomplete multivariate data which does not require distributional assumptions. The proposed test is carried out by comparing the distributions of the observed data across different missing-pattern groups. We prove that the proposed test is consistent against any distributional differences in the observed data. Simulation shows that the proposed procedure has the Type I error well controlled at the nominal level for testing MCAR and also has good power against a variety of non-MCAR alternatives.