{"paper":{"title":"Parameter recovery in two-component contamination mixtures: the $\\mathbb{L}^2$ strategy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Cathy Maugis-Rabusseau, Cl\\'ement Marteau, Jonas Kahn, S\\'ebastien Gadat","submitted_at":"2016-04-01T16:03:11Z","abstract_excerpt":"In this paper, we consider a parametric density contamination model. We work with a sample of i.i.d. data with a common density, $f^\\star =(1-\\lambda^\\star) \\phi + \\lambda^\\star \\phi(.-\\mu^\\star)$, where the shape $\\phi$ is assumed to be known. We establish the optimal rates of convergence for the estimation of the mixture parameters $(\\lambda^\\star,\\mu^\\star)$. In particular, we prove that the classical parametric rate $1/\\sqrt{n}$ cannot be reached when at least one of these parameters is allowed to tend to $0$ with $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00306","kind":"arxiv","version":3},"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"}