{"paper":{"title":"Statistical inference with F-statistics when fitting simple models to high-dimensional data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Hannes Leeb, Lukas Steinberger","submitted_at":"2019-02-12T09:52:48Z","abstract_excerpt":"We study linear subset regression in the context of the high-dimensional overall model $y = \\vartheta+\\theta' z + \\epsilon$ with univariate response $y$ and a $d$-vector of random regressors $z$, independent of $\\epsilon$. Here, \"high-dimensional\" means that the number $d$ of available explanatory variables is much larger than the number $n$ of observations. We consider simple linear sub-models where $y$ is regressed on a set of $p$ regressors given by $x = M'z$, for some $d \\times p$ matrix $M$ of full rank $p < n$. The corresponding simple model, i.e., $y=\\alpha+\\beta' x + e$, can be justifi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04304","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"}