A nonparametric two-sample test using a parametric integral probability metric
For statisticians and machine learning practitioners needing nonparametric two-sample tests, this work offers a new test with competitive performance, though it is an incremental improvement over existing IPM-based tests.
The paper proposes a new two-sample test statistic (PReLU-IPM) based on a parametric integral probability metric using a single-node neural network discriminator, and demonstrates that the resulting test (PReLU-TST) achieves higher or comparable power on simulated and real benchmark datasets compared to existing methods.
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.