{"paper":{"title":"Weighted uniform consistency of kernel density estimators","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Evarist Gine, Joel Zinn, Vladimir Koltchinskii","submitted_at":"2004-10-06T15:52:22Z","abstract_excerpt":"Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \\Psi(t) be a positive continuous function such that \\|\\Psi f^{\\beta}\\|_{\\infty}<\\infty for some 0<\\beta<1/2.\n Under natural smoothness conditions, necessary and sufficient conditions for the sequence \\sqrt\\frac{nh_n^d}{2|\\log h_n^d|}\\|\\Psi(t)(f_n(t)-Ef_n(t))\\|_{\\infty} to be stochastically bounded and to converge a.s. to a constant are obtained.\n Also, the case of larger values of \\beta is studied where a similar sequence with a different norming converges a.s. either to 0 or to +\\inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410170","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"}