U-statistics-based approach for testing the MCAR assumption

Abstract

We present a novel test for assessing whether data follow a pattern of being missing completely at random that was introduced in [1]. The test’s asymptotic properties are derived using the theory of non-degenerate U -statistics. Notably, the novel test statistic aligns with the well-known Little’s statistic when applied to multivariate data with univariate nonresponse. An extensive simulation study evaluates the test’s performance in terms of maintaining type I error rates and statistical power across various scenarios, including different underlying distributions, data dimensions, sample sizes, and alternatives. Little’s MCAR test serves as a benchmark for comparison, revealing that the novel test consistently outperforms it in preserving type I error rates and exhibiting higher empirical power across all studied alternatives.