{"paper":{"title":"Limit Distribution Theory for the Smooth 1-Wasserstein Distance with Applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Kengo Kato, Ritwik Sadhu, Ziv Goldfeld","submitted_at":"2021-07-28T17:02:24Z","abstract_excerpt":"The smooth 1-Wasserstein distance (SWD) $W_1^\\sigma$ was recently proposed as a means to mitigate the curse of dimensionality in empirical approximation while preserving the Wasserstein structure. Indeed, SWD exhibits parametric convergence rates and inherits the metric and topological structure of the classic Wasserstein distance. Motivated by the above, this work conducts a thorough statistical study of the SWD, including a high-dimensional limit distribution result for empirical $W_1^\\sigma$, bootstrap consistency, concentration inequalities, and Berry-Esseen type bounds. The derived nondeg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.13494","kind":"arxiv","version":5},"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/2107.13494/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"}