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Article: Convergence rates of spectral distributions of large sample covariance matrices

TitleConvergence rates of spectral distributions of large sample covariance matrices
Authors
KeywordsConvergence rate
Marčenko-Pastur distribution
Random matrix
Spectral distribution
Issue Date2003
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/simax.php
Citation
SIAM Journal on Matrix Analysis and Applications, 2003, v. 25 n. 1, p. 105-127 How to Cite?
AbstractIn this paper, we improve known results on the convergence rates of spectral distributions of large-dimensional sample covariance matrices of size p × n. Using the Stieltjes transform, we first prove that the expected spectral distribution converges to the limiting Marčenko-Pastur distribution with the dimension sample size ratio y = y n = p/n at a rate of O(n -1/2) if y keeps away from 0 and 1, under the assumption that the entries have a finite eighth moment. Furthermore, the rates for both the convergence in probability and the almost sure convergence are shown to be O p(n -2/5) and o a.s.(n -2/5+η), respectively, when y is away from 1. It is interesting that the rate in all senses is O(n -1/8) when y is close to 1.
Persistent Identifierhttp://hdl.handle.net/10722/132627
ISSN
2023 Impact Factor: 1.5
2023 SCImago Journal Rankings: 1.042
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorBai, ZDen_HK
dc.contributor.authorMiao, Ben_HK
dc.contributor.authorYao, JFen_HK
dc.date.accessioned2011-03-28T09:27:06Z-
dc.date.available2011-03-28T09:27:06Z-
dc.date.issued2003en_HK
dc.identifier.citationSIAM Journal on Matrix Analysis and Applications, 2003, v. 25 n. 1, p. 105-127en_HK
dc.identifier.issn0895-4798en_HK
dc.identifier.urihttp://hdl.handle.net/10722/132627-
dc.description.abstractIn this paper, we improve known results on the convergence rates of spectral distributions of large-dimensional sample covariance matrices of size p × n. Using the Stieltjes transform, we first prove that the expected spectral distribution converges to the limiting Marčenko-Pastur distribution with the dimension sample size ratio y = y n = p/n at a rate of O(n -1/2) if y keeps away from 0 and 1, under the assumption that the entries have a finite eighth moment. Furthermore, the rates for both the convergence in probability and the almost sure convergence are shown to be O p(n -2/5) and o a.s.(n -2/5+η), respectively, when y is away from 1. It is interesting that the rate in all senses is O(n -1/8) when y is close to 1.en_HK
dc.languageengen_US
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/simax.php-
dc.relation.ispartofSIAM Journal on Matrix Analysis and Applicationsen_HK
dc.rights© 2003 Society for Industrial and Applied Mathematics. First Published in SIAM Journal on Matrix Analysis and Applications in volume 25, issue 1, published by the Society for Industrial and Applied Mathematics (SIAM).-
dc.subjectConvergence rateen_HK
dc.subjectMarčenko-Pastur distributionen_HK
dc.subjectRandom matrixen_HK
dc.subjectSpectral distributionen_HK
dc.titleConvergence rates of spectral distributions of large sample covariance matricesen_HK
dc.typeArticleen_HK
dc.identifier.emailYao, JF: jeffyao@hku.hken_HK
dc.identifier.authorityYao, JF=rp01473en_HK
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1137/S0895479801385116en_HK
dc.identifier.scopuseid_2-s2.0-1342310020en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-1342310020&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume25en_HK
dc.identifier.issue1en_HK
dc.identifier.spage105en_HK
dc.identifier.epage127en_HK
dc.identifier.isiWOS:000185130100005-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridBai, ZD=7202524223en_HK
dc.identifier.scopusauthoridMiao, B=7005706366en_HK
dc.identifier.scopusauthoridYao, JF=7403503451en_HK
dc.identifier.issnl0895-4798-

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