{"paper":{"title":"Worst possible sub-directions in high-dimensional models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Sara van de Geer","submitted_at":"2014-03-27T13:41:16Z","abstract_excerpt":"We examine the rate of convergence of the Lasso estimator of lower dimensional components of the high-dimensional parameter. Under bounds on the $\\ell_1$-norm on the worst possible sub-direction these rates are of order $\\sqrt {|J| \\log p / n }$ where $p$ is the total number of parameters, $J \\subset \\{ 1, \\ldots, p \\}$ represents a subset of the parameters and $n$ is the number of observations. We also derive rates in sup-norm in terms of the rate of convergence in $\\ell_1$-norm. The irrepresentable condition on a set $J$ requires that the $\\ell_1$-norm of the worst possible sub-direction is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7023","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"}