{"paper":{"title":"Convergence of Multivariate Quantile Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Adil Ahidar-Coutrix, Philippe Berthet","submitted_at":"2016-07-09T12:36:54Z","abstract_excerpt":"We define the quantile set of order $\\alpha \\in \\left[ 1/2,1\\right) $ associated to a law $P$ on $\\mathbb{R}^{d}$ to be the collection of its directional quantiles seen from an observer $O\\in \\mathbb{R}^{d}$. Under minimal assumptions these star-shaped sets are closed surfaces, continuous in $(O,\\alpha )$ and the collection of empirical quantile surfaces is uniformly consistent.\\ Under mild assumptions -- no density or symmetry is required for $P$ -- our uniform central limit theorem reveals the correlations between quantile points and a non asymptotic Gaussian approximation provides joint con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02604","kind":"arxiv","version":2},"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"}