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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 Date2004
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX
Citation
SIAM Journal On Matrix Analysis And Applications, 2004, 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
2015 Impact Factor: 1.883
2015 SCImago Journal Rankings: 2.052
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.issued2004en_HK
dc.identifier.citationSIAM Journal On Matrix Analysis And Applications, 2004, 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://epubs.siam.org/sam-bin/dbq/toclist/SIMAXen_HK
dc.relation.ispartofSIAM Journal on Matrix Analysis and Applicationsen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
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

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