{"paper":{"title":"The distance between a naive cumulative estimator and its least concave majorant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Eni Musta, Hendrik P. Lopuha\\\"a","submitted_at":"2017-06-16T08:06:37Z","abstract_excerpt":"We consider the process $\\widehat\\Lambda_n-\\Lambda_n$, where $\\Lambda_n$ is a cadlag step estimator for the primitive $\\Lambda$ of a nonincreasing function $\\lambda$ on $[0,1]$, and $\\widehat\\Lambda_n$ is the least concave majorant of $\\Lambda_n$. We extend the results in Kulikov and Lopuha\\\"a (2006, 2008) to the general setting considered in Durot (2007). Under this setting we prove that a suitably scaled version of $\\widehat\\Lambda_n-\\Lambda_n$ converges in distribution to the corresponding process for two-sided Brownian motion with parabolic drift and we establish a central limit theorem fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05173","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"}