{"paper":{"title":"Detection of weak signals in high-dimensional complex-valued data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexei Onatski","submitted_at":"2012-07-30T20:52:45Z","abstract_excerpt":"This paper considers the problem of detecting a few signals in high-dimensional complex-valued Gaussian data satisfying Johnstone's (2001) \\textit{spiked covariance model}. We focus on the difficult case where signals are weak in the sense that the sizes of the corresponding covariance spikes are below the \\textit{phase transition threshold} studied in Baik et al (2005). We derive a simple analytical expression for the maximal possible asymptotic probability of correct detection holding the asymptotic probability of false detection fixed. To accomplish this derivation, we establish what we bel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7098","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"}