{"paper":{"title":"On the efficiency of the de-biased Lasso","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":"2017-08-26T15:30:57Z","abstract_excerpt":"We consider the high-dimensional linear regression model $Y = X \\beta^0 + \\epsilon$ with Gaussian noise $\\epsilon$ and Gaussian random design $X$. We assume that $\\Sigma:= E X^T X / n$ is non-singular and write its inverse as $\\Theta := \\Sigma^{-1}$. The parameter of interest is the first component $\\beta_1^0$ of $\\beta^0$. We show that in the high-dimensional case the asymptotic variance of a debiased Lasso estimator can be smaller than $\\Theta_{1,1}$. For some special such cases we establish asymptotic efficiency. The conditions include $\\beta^0$ being sparse and the first column $\\Theta_1$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07986","kind":"arxiv","version":2},"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"}