Optimal nonparametric testing of Missing Completely At Random, and its connections to compatibility

Abstract

Given a set of incomplete observations, we study the nonparametric problem of testing whether data are Missing Completely At Random (MCAR). Our first contribution is to characterise precisely the set of alternatives that can be distinguished from the MCAR null hypothesis. This reveals interesting and novel links to the theory of Fréchet classes (in particular, compatible distributions) and linear programming, that allow us to propose MCAR tests that are consistent against all detectable alternatives.We define an incompatibility index as a natural measure of ease of detectability, establish its key properties, and show how it can be computed exactly in some cases and bounded in others. Moreover, we prove that our tests can attain the minimax separation rate according to this measure, up to logarithmic factors. Our methodology does not require any complete cases to be effective, and is available in the R package MCARtest.

A Novel Composite DTERM-MDI Model for the Recovery of Missing Data in Internet of Medical Things

“…Berrett et al (8) discussed a nonparametric approach for testing whether data are missing completely at random (MCAR), and its connection to the concept of compatibility. The authors introduced a novel testing procedure for MCAR based on the idea of maximum mean discrepancy (MMD) between the empirical distribution of the observed data and the distribution that would be expected under MCAR.…”