Two-sample distribution tests in high dimensions via max-sliced Wasserstein distance and bootstrapping.

This article focuses on developing a novel two-sample hypothesis test for detecting distributional differences between two high-dimensional populations using the max-sliced Wasserstein distance. The proposed test mitigates the curse of dimensionality by projecting data onto sparse directions and employs a bootstrap procedure to approximate the null distribution, enabling simultaneous confidence intervals that identify both global and marginal distributional differences without additional tests. Theoretical results establish the asymptotic validity and consistency of the test under mild assumptions, allowing the dimension to grow polynomially with sample size, and demonstrate superior power against sparse alternatives compared to existing methods such as maximum mean discrepancy (MMD) and energy distance. Numerical simulations and a real data application to DNA methylation in glioma subtypes illustrate the test’s effectiveness in high-dimensional settings and its ability to pinpoint significant features contributing to distributional shifts.