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Caba\\~na","submitted_at":"2026-05-17T14:22:46Z","abstract_excerpt":"This paper extends a recently proposed family of EDF-based goodness-of-fit procedures for the hypercube $[0,1]^p$ - the m-test and the s-test - which are based on a unique deconstruction of the $p$-parameter Brownian sheet into independent Gaussian processes.\n  We use the fact that whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms. Specifically, we introduce and analyze new procedures derived fr"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Empirical power comparisons show that these extended procedures are highly competitive with existing methods in the statistical literature, demonstrating particular sensitivity to coordinate-based dependencies and joint dependency structures.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Extends m-test and s-test via Brownian sheet deconstruction to new EDF procedures for uniformity on S^p, multivariate normality, symmetry, and independence, with competitive empirical power.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"New EDF tests reduce multivariate normality, symmetry, and independence checks to uniformity testing on the unit hypercube via Brownian sheet decomposition.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6577ec7ade9d531844717ef2abfb03c2d10e82f5708b17adbdd1b0770b56ab34"},"source":{"id":"2605.17474","kind":"arxiv","version":1},"verdict":{"id":"60ac784c-6f25-4477-83bf-8e1a6d76ae6a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:32:18.682872Z","strongest_claim":"Empirical power comparisons show that these extended procedures are highly competitive with existing methods in the statistical literature, demonstrating particular sensitivity to coordinate-based dependencies and joint dependency structures.","one_line_summary":"Extends m-test and s-test via Brownian sheet deconstruction to new EDF procedures for uniformity on S^p, multivariate normality, symmetry, and independence, with competitive empirical power.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms.","pith_extraction_headline":"New EDF tests reduce multivariate normality, symmetry, and independence checks to uniformity testing on the unit hypercube via Brownian sheet decomposition."},"integrity":{"clean":false,"summary":{"advisory":0,"critical":1,"by_detector":{"doi_compliance":{"total":1,"advisory":0,"critical":1,"informational":0}},"informational":0},"endpoint":"/pith/2605.17474/integrity.json","findings":[{"note":"Identifier '10.1137/1.9781611970568' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. 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