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Article: On estimation of the population spectral distribution from a high-dimensional sample covariance matrix

TitleOn estimation of the population spectral distribution from a high-dimensional sample covariance matrix
Authors
KeywordsEigenvalues of covariance matrices
High-dimensional statistics
Marćenko-Pastur distribution
Sample covariance matrices
Issue Date2010
PublisherBlackwell Publishing Asia. The Journal's web site is located at http://www.blackwellpublishing.com/journals/ANZS
Citation
Australian And New Zealand Journal Of Statistics, 2010, v. 52 n. 4, p. 423-437 How to Cite?
AbstractSample covariance matrices play a central role in numerous popular statistical methodologies, for example principal components analysis, Kalman filtering and independent component analysis. However, modern random matrix theory indicates that, when the dimension of a random vector is not negligible with respect to the sample size, the sample covariance matrix demonstrates significant deviations from the underlying population covariance matrix. There is an urgent need to develop new estimation tools in such cases with high-dimensional data to recover the characteristics of the population covariance matrix from the observed sample covariance matrix. We propose a novel solution to this problem based on the method of moments. When the parametric dimension of the population spectrum is finite and known, we prove that the proposed estimator is strongly consistent and asymptotically Gaussian. Otherwise, we combine the first estimation method with a cross-validation procedure to select the unknown model dimension. Simulation experiments demonstrate the consistency of the proposed procedure. We also indicate possible extensions of the proposed estimator to the case where the population spectrum has a density. © 2010 Australian Statistical Publishing Association Inc..
Persistent Identifierhttp://hdl.handle.net/10722/139705
ISSN
2015 Impact Factor: 0.431
2015 SCImago Journal Rankings: 0.275
ISI Accession Number ID
Funding AgencyGrant Number
Chinese National Science Foundation
Northeast Normal University (China)
Region Bretagne (France)
Funding Information:

The authors wish to thank the Chinese National Science Foundation, Northeast Normal University (China) and Region Bretagne (France) for their support of this research.

References

 

DC FieldValueLanguage
dc.contributor.authorBai, Zen_HK
dc.contributor.authorChen, Jen_HK
dc.contributor.authorYao, Jen_HK
dc.date.accessioned2011-09-23T05:54:41Z-
dc.date.available2011-09-23T05:54:41Z-
dc.date.issued2010en_HK
dc.identifier.citationAustralian And New Zealand Journal Of Statistics, 2010, v. 52 n. 4, p. 423-437en_HK
dc.identifier.issn1369-1473en_HK
dc.identifier.urihttp://hdl.handle.net/10722/139705-
dc.description.abstractSample covariance matrices play a central role in numerous popular statistical methodologies, for example principal components analysis, Kalman filtering and independent component analysis. However, modern random matrix theory indicates that, when the dimension of a random vector is not negligible with respect to the sample size, the sample covariance matrix demonstrates significant deviations from the underlying population covariance matrix. There is an urgent need to develop new estimation tools in such cases with high-dimensional data to recover the characteristics of the population covariance matrix from the observed sample covariance matrix. We propose a novel solution to this problem based on the method of moments. When the parametric dimension of the population spectrum is finite and known, we prove that the proposed estimator is strongly consistent and asymptotically Gaussian. Otherwise, we combine the first estimation method with a cross-validation procedure to select the unknown model dimension. Simulation experiments demonstrate the consistency of the proposed procedure. We also indicate possible extensions of the proposed estimator to the case where the population spectrum has a density. © 2010 Australian Statistical Publishing Association Inc..en_HK
dc.languageengen_US
dc.publisherBlackwell Publishing Asia. The Journal's web site is located at http://www.blackwellpublishing.com/journals/ANZSen_HK
dc.relation.ispartofAustralian and New Zealand Journal of Statisticsen_HK
dc.rightsThe definitive version is available at www.blackwell-synergy.com-
dc.subjectEigenvalues of covariance matricesen_HK
dc.subjectHigh-dimensional statisticsen_HK
dc.subjectMarćenko-Pastur distributionen_HK
dc.subjectSample covariance matricesen_HK
dc.titleOn estimation of the population spectral distribution from a high-dimensional sample covariance matrixen_HK
dc.typeArticleen_HK
dc.identifier.emailYao, J: jeffyao@hku.hken_HK
dc.identifier.authorityYao, J=rp01473en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1111/j.1467-842X.2010.00590.xen_HK
dc.identifier.scopuseid_2-s2.0-78650655959en_HK
dc.identifier.hkuros194267en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-78650655959&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume52en_HK
dc.identifier.issue4en_HK
dc.identifier.spage423en_HK
dc.identifier.epage437en_HK
dc.identifier.isiWOS:000285757100005-
dc.publisher.placeAustraliaen_HK
dc.identifier.scopusauthoridBai, Z=7202524223en_HK
dc.identifier.scopusauthoridChen, J=36702620200en_HK
dc.identifier.scopusauthoridYao, J=7403503451en_HK
dc.identifier.citeulike8648015-

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