{"paper":{"title":"Estimating level sets of a distribution function using a plug-in method: a multidimensional extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Elena Di Bernadino (SAF), Thomas Lalo\\\"e (JAD)","submitted_at":"2012-02-09T16:19:43Z","abstract_excerpt":"This paper deals with the problem of estimating the level sets $L(c)= \\{F(x) \\geq c \\}$, with $c \\in (0,1)$, of an unknown distribution function $F$ on \\mathbb{R}^d_+$. A plug-in approach is followed. That is, given a consistent estimator $F_n$ of $F$, we estimate $L(c)$ by $L_n(c)= \\{F_n(x) \\geq c \\}$. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. These results can be considered as generalizations of results previously obtained, in a bivariate framework, in Di Bernardino et al. (2011). Finally we investigate the effects of scal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2035","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"}