{"paper":{"title":"Model selection and estimation of a component in additive regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Xavier Gendre (IMT)","submitted_at":"2012-09-28T14:31:42Z","abstract_excerpt":"Let $Y\\in\\R^n$ be a random vector with mean $s$ and covariance matrix $\\sigma^2P_n\\tra{P_n}$ where $P_n$ is some known $n\\times n$-matrix. We construct a statistical procedure to estimate $s$ as well as under moment condition on $Y$ or Gaussian hypothesis. Both cases are developed for known or unknown $\\sigma^2$. Our approach is free from any prior assumption on $s$ and is based on non-asymptotic model selection methods. Given some linear spaces collection $\\{S_m,\\ m\\in\\M\\}$, we consider, for any $m\\in\\M$, the least-squares estimator $\\hat{s}_m$ of $s$ in $S_m$. Considering a penalty function "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6534","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"}