{"paper":{"title":"Limit Theory for the largest eigenvalues of sample covariance matrices with heavy-tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Oliver Pfaffel, Richard A. Davis, Robert Stelzer","submitted_at":"2011-08-27T16:52:27Z","abstract_excerpt":"We study the joint limit distribution of the $k$ largest eigenvalues of a $p\\times p$ sample covariance matrix $XX^\\T$ based on a large $p\\times n$ matrix $X$. The rows of $X$ are given by independent copies of a linear process, $X_{it}=\\sum_j c_j Z_{i,t-j}$, with regularly varying noise $(Z_{it})$ with tail index $\\alpha\\in(0,4)$. It is shown that a point process based on the eigenvalues of $XX^\\T$ converges, as $n\\to\\infty$ and $p\\to\\infty$ at a suitable rate, in distribution to a Poisson point process with an intensity measure depending on $\\alpha$ and $\\sum c_j^2$. This result is extended "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5464","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"}