{"paper":{"title":"Detecting Rare and Weak Spikes in Large Covariance Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Zheng Tracy Ke","submitted_at":"2016-09-04T01:16:55Z","abstract_excerpt":"Given $p$-dimensional Gaussian vectors $X_i \\stackrel{iid}{\\sim} N(0, \\Sigma)$, $1 \\leq i \\leq n$, where $p \\geq n$, we are interested in testing a null hypothesis where $\\Sigma = I_p$ against an alternative hypothesis where all eigenvalues of $\\Sigma$ are $1$, except for $r$ of them are larger than $1$ (i.e., spiked eigenvalues).\n  We consider a Rare/Weak setting where the spikes are sparse (i.e., $1 \\ll r \\ll p$) and individually weak (i.e., each spiked eigenvalue is only slightly larger than $1$), and discover a phase transition: the two-dimensional phase space that calibrates the spike spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00883","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"}