A Novel Test of Missing Completely at Random: U-statistics-based Approach

Abstract

In this paper, a novel test for testing whether data are Missing Completely at Random is proposed. Asymptotic properties of the test are derived utilizing the theory of non-degenerate U-statistics. It is shown that the novel test statistic coincides with the well-known Little's statistic in the case of a univariate nonresponse. Then, the extensive simulation study is conducted to examine the performance of the test in terms of the preservation of type I error and in terms of power, under various underlying distributions, dimensions of the data and sample sizes. Performance of the Little's MCAR test is used as a benchmark for the comparison. The novel test shows better performance in all of the studied scenarios, better preserving the type I error and having higher empirical powers.