{"paper":{"title":"The Hannan-Quinn Proposition for Linear Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Joe Suzuki","submitted_at":"2010-12-20T10:46:41Z","abstract_excerpt":"We consider the variable selection problem in linear regression. Suppose that we have a set of random variables $X_1,...,X_m,Y,\\epsilon$ such that $Y=\\sum_{k\\in \\pi}\\alpha_kX_k+\\epsilon$ with $\\pi\\subseteq \\{1,...,m\\}$ and $\\alpha_k\\in {\\mathbb R}$ unknown, and $\\epsilon$ is independent of any linear combination of $X_1,...,X_m$. Given actually emitted $n$ examples $\\{(x_{i,1}...,x_{i,m},y_i)\\}_{i=1}^n$ emitted from $(X_1,...,X_m, Y)$, we wish to estimate the true $\\pi$ using information criteria in the form of $H+(k/2)d_n$, where $H$ is the likelihood with respect to $\\pi$ multiplied by -1, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4276","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"}