{"paper":{"title":"Eigenvector overlaps in large sample covariance matrices and nonlinear shrinkage estimators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Guangming Pan, Zeqin Lin","submitted_at":"2024-04-28T13:07:52Z","abstract_excerpt":"Consider a data matrix $Y = [\\mathbf{y}_1, \\cdots, \\mathbf{y}_N]$ of size $M \\times N$, where the columns are independent observations from a random vector $\\mathbf{y}$ with zero mean and population covariance $\\Sigma$. Let $\\mathbf{u}_i$ and $\\mathbf{v}_j$ denote the left and right singular vectors of $Y$, respectively. This study investigates the eigenvector/singular vector overlaps $\\langle {\\mathbf{u}_i, D_1 \\mathbf{u}_j} \\rangle$, $\\langle {\\mathbf{v}_i, D_2 \\mathbf{v}_j} \\rangle$ and $\\langle {\\mathbf{u}_i, D_3 \\mathbf{v}_j} \\rangle$, where $D_k$ are general deterministic matrices with b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.18173","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.18173/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}