{"paper":{"title":"On universal oracle inequalities related to high-dimensional linear models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Yuri Golubev","submitted_at":"2010-11-10T13:57:10Z","abstract_excerpt":"This paper deals with recovering an unknown vector $\\theta$ from the noisy data $Y=A\\theta+\\sigma\\xi$, where $A$ is a known $(m\\times n)$-matrix and $\\xi$ is a white Gaussian noise. It is assumed that $n$ is large and $A$ may be severely ill-posed. Therefore, in order to estimate $\\theta$, a spectral regularization method is used, and our goal is to choose its regularization parameter with the help of the data $Y$. For spectral regularization methods related to the so-called ordered smoothers [see Kneip Ann. Statist. 22 (1994) 835--866], we propose new penalties in the principle of empirical r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2378","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"}