{"paper":{"title":"CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hongtu Zhu, Jianfeng Yao, Shurong Zheng, Zhidong Bai","submitted_at":"2017-08-12T07:41:01Z","abstract_excerpt":"This paper investigates the central limit theorem for linear spectral statistics of high dimensional sample covariance matrices of the form $\\mathbf{B}_n=n^{-1}\\sum_{j=1}^{n}\\mathbf{Q}\\mathbf{x}_j\\mathbf{x}_j^{*}\\mathbf{Q}^{*}$ where $\\mathbf{Q}$ is a nonrandom matrix of dimension $p\\times k$, and $\\{\\mathbf{x}_j\\}$ is a sequence of independent $k$-dimensional random vector with independent entries, under the assumption that $p/n\\to y>0$. A key novelty here is that the dimension $k\\ge p$ can be arbitrary, possibly infinity. This new model of sample covariance matrices $\\mathbf{B}_n$ covers mos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03749","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"}