{"ID":2847629,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.27498","arxiv_id":"2510.27498","title":"Minimax-Optimal Two-Sample Test with Sliced Wasserstein","abstract":"We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees and computational efficiency, its theoretical foundations for hypothesis testing remain limited. We address this gap by proposing a permutation-based SW test and analyzing its performance. The test inherits finite-sample Type I error control from the permutation principle. Moreover, we establish non-asymptotic power bounds and show that the procedure achieves the minimax separation rate $n^{-1/2}$ over multinomial and bounded-support alternatives, matching the optimal guarantees of kernel-based tests while building on the geometric foundations of Wasserstein distances. Our analysis further quantifies the trade-off between the number of projections and statistical power. Finally, numerical experiments demonstrate that the test combines finite-sample validity with competitive power and scalability, and -- unlike kernel-based tests, which require careful kernel tuning -- it performs consistently well across all scenarios we consider.","short_abstract":"We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees and computational efficiency, its theoretical foundations for hypothesis testing...","url_abs":"https://arxiv.org/abs/2510.27498","url_pdf":"https://arxiv.org/pdf/2510.27498v1","authors":"[\"Binh Thuan Tran\",\"Nicolas Schreuder\"]","published":"2025-10-31T14:20:06Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}