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Marcenko-Pastur law for Tyler’s M-estimator

Author(s): Zhang, Teng; Cheng, Xiuyuan; Singer, Amit

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DC FieldValueLanguage
dc.contributor.authorZhang, Teng-
dc.contributor.authorCheng, Xiuyuan-
dc.contributor.authorSinger, Amit-
dc.date.accessioned2019-08-29T17:02:05Z-
dc.date.available2019-08-29T17:02:05Z-
dc.date.issued2016-07en_US
dc.identifier.citationZhang, Teng, Cheng, Xiuyuan, Singer, Amit. (2016). Marcenko-Pastur law for Tyler’s M-estimator. JOURNAL OF MULTIVARIATE ANALYSIS, 149 (114 - 123. doi:10.1016/j.jmva.2016.03.010en_US
dc.identifier.issn0047-259X-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1qf19-
dc.description.abstractThis paper studies the limiting behavior of Tyler’s M-estimator for the scatter matrix, in the regime that the number of samples n and their dimension p both go to infinity, and pin converges to a constant y with 0 < y < 1. We prove that when the data samples, x(1), ... , x(n) are identically and independently generated from the Gaussian distribution (0, 1), the operator norm of the difference between a properly scaled Tyler’s M-estimator and Sigma(n)(i=1)xixi T/n tends to zero. As a result, the spectral distribution of Tyler’s M-estimator converges weakly to the Marcenko-Pastur distribution. (C) 2016 Elsevier Inc. All rights reserved.en_US
dc.format.extent114 - 123en_US
dc.language.isoen_USen_US
dc.relation.ispartofJOURNAL OF MULTIVARIATE ANALYSISen_US
dc.rightsAuthor's manuscripten_US
dc.titleMarcenko-Pastur law for Tyler’s M-estimatoren_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1016/j.jmva.2016.03.010-
dc.date.eissued2016-04-12en_US
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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