Goodness-of-fit testing in incomplete data settings

Abstract

Missing data problems are prevalent across all data-driven fields. While extensive research has been conducted on estimation methods, the literature on goodness-of-fit testing in the presence of missing data remains relatively scarce. In this talk, we explore goodness-of-fit testing under missing data scenarios and provide an overview of recent advancements. We begin by introducing different types of missing data and their mathematical implications. A portion of the talk will be dedicated to one-dimensional goodness-of-fit tests, with a particular focus on randomly right-censored data. Another part will address multivariate settings, emphasizing data missing at random and recent methodological developments in this area. In both cases, we aim to answer a fundamental question: is it more effective to impute missing data or to adapt the underlying test statistics? To this end, we discuss the advantages and limitations of both approaches. Since most test statistics in this context are closely linked to U-statistics, we will also present key asymptotic results for U-statistics in multivariate settings. Finally, the talk will conclude with an overview of current research directions and open challenges, highlighting potential avenues for future work.