{"paper":{"title":"Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Guangming Pan, Jiang Hu, Wang Zhou, Zhigang Bao","submitted_at":"2017-04-08T00:30:09Z","abstract_excerpt":"Consider a Gaussian vector $\\mathbf{z}=(\\mathbf{x}',\\mathbf{y}')'$, consisting of two sub-vectors $\\mathbf{x}$ and $\\mathbf{y}$ with dimensions $p$ and $q$ respectively, where both $p$ and $q$ are proportional to the sample size $n$. Denote by $\\Sigma_{\\mathbf{u}\\mathbf{v}}$ the population cross-covariance matrix of random vectors $\\mathbf{u}$ and $\\mathbf{v}$, and denote by $S_{\\mathbf{u}\\mathbf{v}}$ the sample counterpart. The canonical correlation coefficients between $\\mathbf{x}$ and $\\mathbf{y}$ are known as the square roots of the nonzero eigenvalues of the canonical correlation matrix $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02408","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"}