{"paper":{"title":"Joint CLT for eigenvalue statistics from several dependent large dimensional sample covariance matrices with application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jianfeng Yao, Weiming Li, Zeng Li","submitted_at":"2018-01-20T06:27:59Z","abstract_excerpt":"Let $\\mathbf{X}_n=(x_{ij})$ be a $k \\times n$ data matrix with complex-valued, independent and standardized entries satisfying a Lindeberg-type moment condition. We consider simultaneously $R$ sample covariance matrices $\\mathbf{B}_{nr}=\\frac1n \\mathbf{Q}_r \\mathbf{X}_n \\mathbf{X}_n^*\\mathbf{Q}_r^\\top,~1\\le r\\le R$, where the $\\mathbf{Q}_{r}$'s are nonrandom real matrices with common dimensions $p\\times k~(k\\geq p)$. Assuming that both the dimension $p$ and the sample size $n$ grow to infinity, the limiting distributions of the eigenvalues of the matrices $\\{\\mathbf{B}_{nr}\\}$ are identified, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06634","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"}