A nonparametric two-sample test using a parametric integral probability metric

Abstract:Detecting distributional differences between two independent samples is a fundamental problem in statistics and machine learning. Nonparametric two-sample testing provides a principled framework for determining whether two samples are drawn from the same underlying distribution, without assuming any specific parametric form for the distribution. In this study, we propose a new two-sample test statistic based on a newly introduced integral probability metric (IPM), using a specially designed parametric discriminator class with a single node of a neural network. We show that the resulting test statistic, called PReLU-IPM, is nonparametric and establish theoretical guarantees for the associated two-sample testing procedure, PReLU-TST, including its consistency and asymptotical equivalence to nonparametric IPM-based tests under regularity conditions. By analyzing multiple simulated and real benchmark datasets, we demonstrate that PReLU-TST achieves higher power across a range of alternatives or performs comparably to its competitors, for finite samples.

45 pages. Accepted for publication in Statistical Analysis and Data Mining

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2606.16941 [stat.ML]

(or arXiv:2606.16941v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2606.16941 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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