Addressing missing data challenges: A multivariate goodness-of-fit testing perspective

Abstract

The problem of missing data is common when dealing with real data sets. Therefore it attracted the attention of scientists across various disciplines. However, its implications on goodness-of-fit testing remain relatively unexplored. In this study, we aim to bridge this gap in the literature by examining modifications to some commonly used tests designed for complete data to accommodate missingness issues. Our objectives are twofold: to demonstrate that the impact of imputation procedures remains significant across all types of missingness and to investigate the properties of test modifications under the assumption of missing completely at random (MCAR) data. Our findings, which include insights into the limiting null distributions for modified characteristic-function-based tests and extensive power analyses, lead to general recommendations for addressing missing data challenges within the context of goodness-of-fit testing.