{"paper":{"title":"On empirical distribution function of high-dimensional Gaussian vector components with an application to multiple testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Etienne Roquain (LPMA), Sylvain Delattre (LPMA)","submitted_at":"2012-10-09T04:29:23Z","abstract_excerpt":"This paper introduces a new framework to study the asymptotical behavior of the empirical distribution function (e.d.f.) of Gaussian vector components, whose correlation matrix $\\Gamma^{(m)}$ is dimension-dependent. Hence, by contrast with the existing literature, the vector is not assumed to be stationary. Rather, we make a \"vanishing second order\" assumption ensuring that the covariance matrix $\\Gamma^{(m)}$ is not too far from the identity matrix, while the behavior of the e.d.f. is affected by $\\Gamma^{(m)}$ only through the sequence $\\gamma_m=m^{-2} \\sum_{i\\neq j} \\Gamma_{i,j}^{(m)}$, as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2489","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"}