Homogeneity testing in the presence of missing data

Abstract

Here, we explore the problem of homogeneity testing when data are subject to missingness under various missing data mechanisms. We focus on energy distance-based tests and their generalizations. Beyond the standard complete-case approach, we propose a novel adaptation of the energy test statistic that takes advantage of all available information. Appropriate resampling-based approaches are developed for p-value approximation in this setting. Additionally, we introduce a tailored bootstrap procedure designed for settings where the test statistic is evaluated on datasets that have been imputed using common imputation techniques. An extensive simulation study examines the performance of the proposed methods across various sample sizes, dimensions, underlying distributions, missingness mechanisms, and proportions of missing data. Based on the findings, we provide practical recommendations to guide the use of homogeneity tests in scenarios with incomplete data.