{"paper":{"title":"A unified matrix model including both CCA and F matrices in multivariate analysis: the largest eigenvalue and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Guangming Pan, Qing Yang, Xiao Han","submitted_at":"2016-06-14T15:16:13Z","abstract_excerpt":"Let $\\bbZ_{M_1\\times N}=\\bbT^{\\frac{1}{2}}\\bbX$ where $(\\bbT^{\\frac{1}{2}})^2=\\bbT$ is a positive definite matrix and $\\bbX$ consists of independent random variables with mean zero and variance one. This paper proposes a unified matrix model $$\\bold{\\bbom}=(\\bbZ\\bbU_2\\bbU_2^T\\bbZ^T)^{-1}\\bbZ\\bbU_1\\bbU_1^T\\bbZ^T,$$ where $\\bbU_1$ and $\\bbU_2$ are isometric with dimensions $N\\times N_1$ and $N\\times (N-N_2)$ respectively such that $\\bbU_1^T\\bbU_1=\\bbI_{N_1}$, $\\bbU_2^T\\bbU_2=\\bbI_{N-N_2}$ and $\\bbU_1^T\\bbU_2=0$. Moreover, $\\bbU_1$ and $\\bbU_2$ (random or non-random) are independent of $\\bbZ_{M_1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04417","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"}