{"paper":{"title":"The Spatial Cram'{e}r--von Mises Test of Independence under $\\beta$-Mixing: Asymptotic Theory and Python Implementation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Marco Mandap","submitted_at":"2026-05-18T22:32:52Z","abstract_excerpt":"We derive the asymptotic distribution of the spatial Cram'{e}r--von Mises statistic for testing bivariate independence in stationary random fields on $\\mathbb{R}^2$ under polynomial $\\beta$-mixing dependence, and document the Python implementation that reproduces all simulation results. The classical test assumes i.i.d. observations; we extend it to spatially dependent data by combining three ingredients: (i) a Davydov-type covariance bound yielding integrability of the spatial covariance kernel under $\\theta > 2(2+\\delta)/\\delta$; (ii) a reformulation of the inner-form test statistic as a deg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19164","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/2605.19164/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"}