{"paper":{"title":"Strong noise estimation in cubic splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Aziz El Kaabouchi, Azzouz Dermoune","submitted_at":"2014-06-06T10:15:47Z","abstract_excerpt":"The data $(y_i,x_i)\\in$ $\\textbf{R}\\times[a,b]$, $i=1,\\ldots,n$ satisfy $y_i=s(x_i)+e_i$ where $s$ belongs to the set of cubic splines. The unknown noises $(e_i)$ are such that $var(e_I)=1$ for some $I\\in \\{1, \\ldots, n\\}$ and $var(e_i)=\\sigma^2$ for $i\\neq I$. We suppose that the most important noise is $e_I$, i.e. the ratio $r_I=\\frac{1}{\\sigma^2}$ is larger than one. If the ratio $r_I$ is large, then we show, for all smoothing parameter, that the penalized least squares estimator of the $B$-spline basis recovers exactly the position $I$ and the sign of the most important noise $e_I$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1629","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"}