{"paper":{"title":"Spectral statistics of large dimensional Spearman's rank correlation matrix and its application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Guangming Pan, Liang-Ching Lin, Wang Zhou, Zhigang Bao","submitted_at":"2013-12-18T12:55:28Z","abstract_excerpt":"Let $\\mathbf{Q}=(Q_1,\\ldots,Q_n)$ be a random vector drawn from the uniform distribution on the set of all $n!$ permutations of $\\{1,2,\\ldots,n\\}$. Let $\\mathbf{Z}=(Z_1,\\ldots,Z_n)$, where $Z_j$ is the mean zero variance one random variable obtained by centralizing and normalizing $Q_j$, $j=1,\\ldots,n$. Assume that $\\mathbf {X}_i,i=1,\\ldots ,p$ are i.i.d. copies of $\\frac{1}{\\sqrt{p}}\\mathbf{Z}$ and $X=X_{p,n}$ is the $p\\times n$ random matrix with $\\mathbf{X}_i$ as its $i$th row. Then $S_n=XX^*$ is called the $p\\times n$ Spearman's rank correlation matrix which can be regarded as a high dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5119","kind":"arxiv","version":3},"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"}