{"paper":{"title":"Explicit confidence bands and intervals for distribution functions and their derivatives via random Weierstrass-type operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"C. Sang\\\"uesa, Jos\\'e A. Adell, J. T. Alcal\\'a","submitted_at":"2026-06-23T09:37:28Z","abstract_excerpt":"Classical kernel estimators of second order are interpreted in terms of random Weierstrass-type operators, particularly random Steklov operators. This leads us to obtain explicit nonasymptotic confidence bands and intervals for distribution functions $F$ and their derivatives $F^{(k)}$. Under the only assumption that $F^{(k)}$ is uniformly continuous, confidence bands for $F^{(k)}$ are established by using the Dvoretzky-Kiefer-Wolfowitz inequality. To give confidence intervals, we allow $F^{(k)}$ to have isolated discontinuities of the first kind, so that we really estimate the midpoint functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24345","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/2606.24345/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"}