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Article: Strong convergence of ESD for the generalized sample covariance matrices when p/n→0

TitleStrong convergence of ESD for the generalized sample covariance matrices when p/n→0
Authors
KeywordsLimiting spectral distribution
Sample covariance matrix
Stieltjes transform
Issue Date2012
Citation
Statistics and Probability Letters, 2012, v. 82, n. 5, p. 894-901 How to Cite?
AbstractLet X=[X ij]p×n be a p× n random matrix whose entries are i.i.d real random variables satisfying the moment condition E{double-struck}X 114<∞. Let T be a p× p deterministic nonnegative definite matrix. It is assumed that the empirical distribution of the eigenvalues of T converges weakly to a probability distribution. We consider the renormalized sample covariance matrix H̃=√n/p(1/nT 1/2XX tT 1/2-T) in the case of p/n→ 0 as p, n→ ∞. We study the limiting spectral distribution of H in this paper. The limiting distribution is shown to be coincident with the case of a generalized Wigner matrix considered in. Bai and Zhang (2010). © 2012 Elsevier B.V..
Persistent Identifierhttp://hdl.handle.net/10722/348961
ISSN
2023 Impact Factor: 0.9
2023 SCImago Journal Rankings: 0.448

 

DC FieldValueLanguage
dc.contributor.authorBao, Zhigang-
dc.date.accessioned2024-10-17T06:55:13Z-
dc.date.available2024-10-17T06:55:13Z-
dc.date.issued2012-
dc.identifier.citationStatistics and Probability Letters, 2012, v. 82, n. 5, p. 894-901-
dc.identifier.issn0167-7152-
dc.identifier.urihttp://hdl.handle.net/10722/348961-
dc.description.abstractLet X=[X ij]p×n be a p× n random matrix whose entries are i.i.d real random variables satisfying the moment condition E{double-struck}X 114<∞. Let T be a p× p deterministic nonnegative definite matrix. It is assumed that the empirical distribution of the eigenvalues of T converges weakly to a probability distribution. We consider the renormalized sample covariance matrix H̃=√n/p(1/nT 1/2XX tT 1/2-T) in the case of p/n→ 0 as p, n→ ∞. We study the limiting spectral distribution of H in this paper. The limiting distribution is shown to be coincident with the case of a generalized Wigner matrix considered in. Bai and Zhang (2010). © 2012 Elsevier B.V..-
dc.languageeng-
dc.relation.ispartofStatistics and Probability Letters-
dc.subjectLimiting spectral distribution-
dc.subjectSample covariance matrix-
dc.subjectStieltjes transform-
dc.titleStrong convergence of ESD for the generalized sample covariance matrices when p/n→0-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.spl.2012.01.012-
dc.identifier.scopuseid_2-s2.0-84857251607-
dc.identifier.volume82-
dc.identifier.issue5-
dc.identifier.spage894-
dc.identifier.epage901-

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