{"paper":{"title":"Canonical correlation coefficients of high-dimensional normal vectors: finite rank case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Guangming Pan, Jiang Hu, Wang Zhou, Zhigang Bao","submitted_at":"2014-07-27T07:17:30Z","abstract_excerpt":"Consider a normal vector $\\mathbf{z}=(\\mathbf{x}',\\mathbf{y}')'$, consisting of two sub-vectors $\\mathbf{x}$ and $\\mathbf{y}$ with dimensions $p$ and $q$ respectively. With $n$ independent observations of $\\mathbf{z}$ at hand, we study the correlation between $\\mathbf{x}$ and $\\mathbf{y}$, from the perspective of the Canonical Correlation Analysis, under the high-dimensional setting: both $p$ and $q$ are proportional to the sample size $n$. In this paper, we focus on the case that $\\Sigma_{\\mathbf{x}\\mathbf{y}}$ is of finite rank $k$, i.e. there are $k$ nonzero canonical correlation coefficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7194","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"}