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Article: Moment approach for singular values distribution of a large auto-covariance matrix

TitleMoment approach for singular values distribution of a large auto-covariance matrix
Authors
Issue Date2016
PublisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/aihp/default.htm
Citation
Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 2016, v. 52 n. 4, p. 1641-1666 How to Cite?
AbstractLet (εt)t>0(εt)t>0 be a sequence of independent real random vectors of pp-dimension and let XT=∑s+Tt=s+1εtε∗t−s/TXT=∑t=s+1s+Tεtεt−s∗/T be the lag-ss (ss is a fixed positive integer) auto-covariance matrix of εtεt. Since XTXT is not symmetric, we consider its singular values, which are the square roots of the eigenvalues of XTX∗TXTXT∗. Using the method of moments, we are able to investigate the limiting behaviors of the eigenvalues of XTX∗TXTXT∗ in two aspects. First, we show that the empirical spectral distribution of its eigenvalues converges to a nonrandom limit FF, which is a result previously developed in (J. Multivariate Anal. 137 (2015) 119–140) using the Stieltjes transform method. Second, we establish the convergence of its largest eigenvalue to the right edge of FF.
Persistent Identifierhttp://hdl.handle.net/10722/231312
ISSN
2015 Impact Factor: 0.938
2015 SCImago Journal Rankings: 1.716

 

DC FieldValueLanguage
dc.contributor.authorWang, Q-
dc.contributor.authorYao, JJ-
dc.date.accessioned2016-09-20T05:22:15Z-
dc.date.available2016-09-20T05:22:15Z-
dc.date.issued2016-
dc.identifier.citationAnnales de l'Institut Henri Poincaré Probabilités et Statistiques, 2016, v. 52 n. 4, p. 1641-1666-
dc.identifier.issn0246-0203-
dc.identifier.urihttp://hdl.handle.net/10722/231312-
dc.description.abstractLet (εt)t>0(εt)t>0 be a sequence of independent real random vectors of pp-dimension and let XT=∑s+Tt=s+1εtε∗t−s/TXT=∑t=s+1s+Tεtεt−s∗/T be the lag-ss (ss is a fixed positive integer) auto-covariance matrix of εtεt. Since XTXT is not symmetric, we consider its singular values, which are the square roots of the eigenvalues of XTX∗TXTXT∗. Using the method of moments, we are able to investigate the limiting behaviors of the eigenvalues of XTX∗TXTXT∗ in two aspects. First, we show that the empirical spectral distribution of its eigenvalues converges to a nonrandom limit FF, which is a result previously developed in (J. Multivariate Anal. 137 (2015) 119–140) using the Stieltjes transform method. Second, we establish the convergence of its largest eigenvalue to the right edge of FF.-
dc.languageeng-
dc.publisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/aihp/default.htm-
dc.relation.ispartofAnnales de l'Institut Henri Poincaré Probabilités et Statistiques-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.titleMoment approach for singular values distribution of a large auto-covariance matrix-
dc.typeArticle-
dc.identifier.emailYao, JJ: jeffyao@hku.hk-
dc.identifier.authorityYao, JJ=rp01473-
dc.description.naturepublished_or_final_version-
dc.identifier.hkuros263170-
dc.identifier.volume52-
dc.identifier.issue4-
dc.identifier.spage1641-
dc.identifier.epage1666-
dc.publisher.placeUnited States-

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