A permutation test that aggregates per-client Wasserstein distances into an integrated transportation distance detects distributional differences in distributed data, with claimed Type I error control and high power.
On wasserstein two sample testing and related families of nonparametric tests
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Leveraging Optimal Transport for Distributed Two-Sample Testing: An Integrated Transportation Distance-based Framework
A permutation test that aggregates per-client Wasserstein distances into an integrated transportation distance detects distributional differences in distributed data, with claimed Type I error control and high power.