{"paper":{"title":"Ensemble-based estimates of eigenvector error for empirical covariance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.PR","stat.AP","stat.TH"],"primary_cat":"math.ST","authors_text":"Dane Taylor, Francois G. Meyer, Juan G. Restrepo","submitted_at":"2016-12-28T05:04:35Z","abstract_excerpt":"Covariance matrices are fundamental to the analysis and forecast of economic, physical and biological systems. Although the eigenvalues $\\{\\lambda_i\\}$ and eigenvectors $\\{{\\bf u}_i\\}$ of a covariance matrix are central to such endeavors, in practice one must inevitably approximate the covariance matrix based on data with finite sample size $n$ to obtain empirical eigenvalues $\\{\\tilde{\\lambda}_i\\}$ and eigenvectors $\\{\\tilde{{\\bf u}}_i\\}$, and therefore understanding the error so introduced is of central importance. We analyze eigenvector error $\\|{\\bf u}_i - \\tilde{{\\bf u}}_i \\|^2$ while lev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08804","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"}