{"paper":{"title":"A Strong Invariance Theorem of the Tail Empirical Copula Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP","stat.TH"],"primary_cat":"math.ST","authors_text":"Salim Bouzebda, Tarek Zari","submitted_at":"2011-10-15T20:14:00Z","abstract_excerpt":"We study the behavior of bivariate empirical copula process $\\mathbb{G}_n(\\cdot,\\cdot)$ on pavements $[0,k_n/n]^2$ of $[0,1]^2,$ where $k_n$ is a sequence of positive constants fulfilling some conditions. We provide a upper bound for the strong approximation of $\\mathbb{G}_n(\\cdot,\\cdot)$ by a Gaussian process when $k_n/n \\searrow \\gamma$ as $n\\rightarrow \\infty,$ where $0 \\leq \\gamma \\leq 1.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3437","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":""},"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"}