{"paper":{"title":"On the principal components of sample covariance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Alex Bloemendal, Antti Knowles, Horng-Tzer Yau, Jun Yin","submitted_at":"2014-04-03T07:41:08Z","abstract_excerpt":"We introduce a class of $M \\times M$ sample covariance matrices $\\mathcal Q$ which subsumes and generalizes several previous models. The associated population covariance matrix $\\Sigma = \\mathbb E \\cal Q$ is assumed to differ from the identity by a matrix of bounded rank. All quantities except the rank of $\\Sigma - I_M$ may depend on $M$ in an arbitrary fashion. We investigate the principal components, i.e.\\ the top eigenvalues and eigenvectors, of $\\mathcal Q$. We derive precise large deviation estimates on the generalized components $\\langle \\mathbf w, \\boldsymbol \\xi_i \\rangle$ of the outli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0788","kind":"arxiv","version":3},"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"}