{"paper":{"title":"On the Bernstein-smoothed lower-tail Spearman's rho estimator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Fr\\'ed\\'eric Ouimet, Selim Orhun Susam","submitted_at":"2025-06-10T14:46:50Z","abstract_excerpt":"This note develops a Bernstein estimator for lower-tail Spearman's rho and establishes its strong consistency and asymptotic normality under mild regularity conditions. Smoothing the empirical copula yields a strictly smaller mean squared error (MSE) in tail regions by lowering sampling variance relative to the classical Spearman's rho estimator. A Monte Carlo simulation experiment with the Farlie--Gumbel--Morgenstern copula demonstrates variance reductions that translate into lower MSE estimates (up to $\\sim 70\\%$ lower) at deep-tail thresholds under weak to moderate dependence and small samp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08857","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/2506.08857/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"}