{"paper":{"title":"New asymptotic results in principal component analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Karim Lounici, Vladimir Koltchinskii","submitted_at":"2016-01-07T09:30:15Z","abstract_excerpt":"Let $X$ be a mean zero Gaussian random vector in a separable Hilbert space ${\\mathbb H}$ with covariance operator $\\Sigma:={\\mathbb E}(X\\otimes X).$ Let $\\Sigma=\\sum_{r\\geq 1}\\mu_r P_r$ be the spectral decomposition of $\\Sigma$ with distinct eigenvalues $\\mu_1>\\mu_2> \\dots$ and the corresponding spectral projectors $P_1, P_2, \\dots.$ Given a sample $X_1,\\dots, X_n$ of size $n$ of i.i.d. copies of $X,$ the sample covariance operator is defined as $\\hat \\Sigma_n := n^{-1}\\sum_{j=1}^n X_j\\otimes X_j.$ The main goal of principal component analysis is to estimate spectral projectors $P_1, P_2, \\dot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01457","kind":"arxiv","version":1},"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"}