Testing the distribution change in multivariate data using rank energy statistics

This paper focuses on detecting and locating any distribution change in multivariate data when there is at most one change point. A nonparametric test is proposed utilizing a novel rank energy statistic, which is constructed based on multivariate ranks defined using the measure transportation theory. Theoretical results show that its asymptotic null distribution is independent of the underlying data-generating distribution, thus exhibiting an exact distribution-free property. This enables us to develop a computationally feasible algorithm for computing universal rejection thresholds across different sample sizes, particularly for long data sequences. We also establish a consistency theory for estimated change point location. Extensive simulation studies show that our proposed test performs robustly across various settings, especially for heavy-tailed distributions. A real data application for a financial data set is carried out to confirm its validity.