{"paper":{"title":"Wasserstein-Based Test for Empirical Measure Convergence of Dependent Sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A Wasserstein-1 statistic tests convergence of empirical measures from stationary dependent sequences.","cross_cats":[],"primary_cat":"stat.AP","authors_text":"Alexander Yordanov, Peter Hristov","submitted_at":"2026-04-03T03:49:40Z","abstract_excerpt":"We develop Wasserstein-based hypothesis tests for empirical-measure convergence in stationary dependent sequences. For a known candidate invariant measure, $\\mu$, we study the statistic $T_n=\\sqrt{n}\\,W_1(\\hat\\mu_n,\\mu)$ and establish asymptotic level-$\\alpha$ validity under the null, together with consistency under fixed alternatives. When the invariant measure is unknown, we derive the asymptotic law of the pairwise statistic $\\sqrt{n}\\,W_1(\\hat\\mu_n^{(i)},\\hat\\mu_n^{(j)})$ for independent trajectories and obtain a corresponding pairwise test, including Bonferroni control for multiple compar"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish asymptotic level-α validity under the null, together with consistency under fixed alternatives for the statistic T_n = sqrt(n) W_1(μ̂_n, μ).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The underlying sequence is stationary and possesses an invariant probability measure μ (implicit in the setup for both known and unknown cases).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Wasserstein-based tests for empirical measure convergence in stationary dependent sequences, with asymptotic level-alpha validity for known measures and pairwise tests for unknown measures.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A Wasserstein-1 statistic tests convergence of empirical measures from stationary dependent sequences.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"809dfe5fa9dfcb3fd5d8e1efae628ac1e3a05b822ca9a4fed3594e54f4cf70d5"},"source":{"id":"2604.02700","kind":"arxiv","version":2},"verdict":{"id":"6afdfca5-11e6-4332-b0d1-c3452f478e57","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T19:14:57.987643Z","strongest_claim":"We establish asymptotic level-α validity under the null, together with consistency under fixed alternatives for the statistic T_n = sqrt(n) W_1(μ̂_n, μ).","one_line_summary":"Wasserstein-based tests for empirical measure convergence in stationary dependent sequences, with asymptotic level-alpha validity for known measures and pairwise tests for unknown measures.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The underlying sequence is stationary and possesses an invariant probability measure μ (implicit in the setup for both known and unknown cases).","pith_extraction_headline":"A Wasserstein-1 statistic tests convergence of empirical measures from stationary dependent sequences."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.02700/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":2,"snapshot_sha256":"c6838563cc0c84148c3e95582d3e92d2f787b3077fdc81211827e284744e1318"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}