{"paper":{"title":"When Do Generalized Permutation Tests Achieve Optimal Power? A Dispersion Characterization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Ilmun Kim, Yongmin Kim","submitted_at":"2026-05-30T07:03:58Z","abstract_excerpt":"We study generalized Monte Carlo permutation tests under a non-uniform distribution on permutations. Focusing on the difference-in-means statistic, we introduce two scalar dispersion measures that quantify departures from complete randomization at the individual and pairwise levels. We show that if both dispersions vanish asymptotically, then the conditional permutation distribution converges to its Gaussian benchmark, the critical value stabilizes, and the test attains optimal Pitman local power. Conversely, if these dispersions fail to vanish, the permutation distribution does not self-avera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00578","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.00578/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}