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

• URL: http://arxiv.org/abs/2606.16941v1
• Date: Mon, 15 Jun 2026 16:42:57 GMT
• Title: A nonparametric two-sample test using a parametric integral probability metric
• Abstract summary: We propose a new two-sample test statistic based on a newly introduced integral probability metric (IPM)<n>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.
• Score: 10.249944506187989
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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