{"paper":{"title":"On singular value distribution of large dimensional auto-covariance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Guangming Pan, Jianfeng Yao, Zeng Li","submitted_at":"2014-02-25T12:32:28Z","abstract_excerpt":"Let $(\\varepsilon_j)_{j\\geq 0}$ be a sequence of independent $p-$dimensional random vectors and $\\tau\\geq1$ a given integer. From a sample $\\varepsilon_1,\\cdots,\\varepsilon_{T+\\tau-1},\\varepsilon_{T+\\tau}$ of the sequence, the so-called lag $-\\tau$ auto-covariance matrix is $C_{\\tau}=T^{-1}\\sum_{j=1}^T\\varepsilon_{\\tau+j}\\varepsilon_{j}^t$. When the dimension $p$ is large compared to the sample size $T$, this paper establishes the limit of the singular value distribution of $C_\\tau$ assuming that $p$ and $T$ grow to infinity proportionally and the sequence satisfies a Lindeberg condition on fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6149","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"}