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Article: Central limit theorems for eigenvalues in a spiked population model

TitleCentral limit theorems for eigenvalues in a spiked population model
Authors
KeywordsCentral limit theorems
Extreme eigenvalues
Largest eigenvalue
Random quadratic forms
Random sesquilinear forms
Sample covariance matrices
Spiked population model
Issue Date2008
PublisherElsevier France, Editions Scientifiques et Medicales. The Journal's web site is located at http://www.elsevier.com/locate/anihpb
Citation
Annales De L'institut Henri Poincare (B) Probability And Statistics, 2008, v. 44 n. 3, p. 447-474 How to Cite?
AbstractIn a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the population and the sample sizes become large. This paper establishes the limiting distributions of these extreme sample eigenvalues. As another important result of the paper, we provide a central limit theorem on random sesquilinear forms. © Association des Publications de l'Institut Henri Poincaré, 2008.
Persistent Identifierhttp://hdl.handle.net/10722/132611
ISSN
2015 Impact Factor: 0.938
2015 SCImago Journal Rankings: 1.716
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorBai, Zen_HK
dc.contributor.authorYao, JFen_HK
dc.date.accessioned2011-03-28T09:27:00Z-
dc.date.available2011-03-28T09:27:00Z-
dc.date.issued2008en_HK
dc.identifier.citationAnnales De L'institut Henri Poincare (B) Probability And Statistics, 2008, v. 44 n. 3, p. 447-474en_HK
dc.identifier.issn0246-0203en_HK
dc.identifier.urihttp://hdl.handle.net/10722/132611-
dc.description.abstractIn a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the population and the sample sizes become large. This paper establishes the limiting distributions of these extreme sample eigenvalues. As another important result of the paper, we provide a central limit theorem on random sesquilinear forms. © Association des Publications de l'Institut Henri Poincaré, 2008.en_HK
dc.languageengen_US
dc.publisherElsevier France, Editions Scientifiques et Medicales. The Journal's web site is located at http://www.elsevier.com/locate/anihpben_HK
dc.relation.ispartofAnnales de l'institut Henri Poincare (B) Probability and Statisticsen_HK
dc.subjectCentral limit theoremsen_HK
dc.subjectExtreme eigenvaluesen_HK
dc.subjectLargest eigenvalueen_HK
dc.subjectRandom quadratic formsen_HK
dc.subjectRandom sesquilinear formsen_HK
dc.subjectSample covariance matricesen_HK
dc.subjectSpiked population modelen_HK
dc.titleCentral limit theorems for eigenvalues in a spiked population modelen_HK
dc.typeArticleen_HK
dc.identifier.emailYao, JF: jeffyao@hku.hken_HK
dc.identifier.authorityYao, JF=rp01473en_HK
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1214/07-AIHP118en_HK
dc.identifier.scopuseid_2-s2.0-63849341672en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-63849341672&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume44en_HK
dc.identifier.issue3en_HK
dc.identifier.spage447en_HK
dc.identifier.epage474en_HK
dc.identifier.isiWOS:000256781500003-
dc.publisher.placeFranceen_HK
dc.identifier.scopusauthoridBai, Z=7202524223en_HK
dc.identifier.scopusauthoridYao, JF=7403503451en_HK

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