{"paper":{"title":"Asymptotic behavior of unregularized and ridge-regularized high-dimensional robust regression estimators : rigorous results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Noureddine El Karoui","submitted_at":"2013-11-11T14:04:06Z","abstract_excerpt":"We study the behavior of high-dimensional robust regression estimators in the asymptotic regime where $p/n$ tends to a finite non-zero limit. More specifically, we study ridge-regularized estimators, i.e $\\widehat{\\beta}=\\text{argmin}_{\\beta \\in \\mathbb{R}^p} \\frac{1}{n}\\sum_{i=1}^n \\rho(\\varepsilon_i-X_i' \\beta)+\\frac{\\tau}{2}\\lVert\\beta\\rVert^2$. In a recently published paper, we had developed with collaborators probabilistic heuristics to understand the asymptotic behavior of $\\widehat{\\beta}$. We give here a rigorous proof, properly justifying all the arguments we had given in that paper. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2445","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"}