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Article: Asymptotic distributions of principal components based on robust dispersions

TitleAsymptotic distributions of principal components based on robust dispersions
Authors
KeywordsAsymptotic normality
Dispersion
Principal component
Projection pursuit
Robustness
Issue Date2003
PublisherOxford University Press. The Journal's web site is located at http://biomet.oxfordjournals.org/
Citation
Biometrika, 2003, v. 90 n. 4, p. 953-966 How to Cite?
AbstractAlgebraically, principal components can be defined as the eigenvalues and eigenvectors of a covariance or correlation matrix, but they are statistically meaningful as successive projections of the multivariate data in the direction of maximal variability. An attractive alternative in robust principal component analysis is to replace the classical variability measure, i.e. variance, by a robust dispersion measure. This projection-pursuit approach was first proposed in Li & Chen (1985) as a method of constructing a robust scatter matrix. Recent unpublished work of C. Croux and A. Ruiz-Gazen provided the influence functions of the resulting principal components. The present paper focuses on the asymptotic distributions of robust principal components. In particular, we obtain the asymptotic normality of the principal components that maximise a robust dispersion measure. We also explain the need to use a dispersion functional with a continuous influence function.
Persistent Identifierhttp://hdl.handle.net/10722/82714
ISSN
2015 Impact Factor: 1.13
2015 SCImago Journal Rankings: 2.801
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorCui, Hen_HK
dc.contributor.authorHe, Xen_HK
dc.contributor.authorNg, KWen_HK
dc.date.accessioned2010-09-06T08:32:33Z-
dc.date.available2010-09-06T08:32:33Z-
dc.date.issued2003en_HK
dc.identifier.citationBiometrika, 2003, v. 90 n. 4, p. 953-966en_HK
dc.identifier.issn0006-3444en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82714-
dc.description.abstractAlgebraically, principal components can be defined as the eigenvalues and eigenvectors of a covariance or correlation matrix, but they are statistically meaningful as successive projections of the multivariate data in the direction of maximal variability. An attractive alternative in robust principal component analysis is to replace the classical variability measure, i.e. variance, by a robust dispersion measure. This projection-pursuit approach was first proposed in Li & Chen (1985) as a method of constructing a robust scatter matrix. Recent unpublished work of C. Croux and A. Ruiz-Gazen provided the influence functions of the resulting principal components. The present paper focuses on the asymptotic distributions of robust principal components. In particular, we obtain the asymptotic normality of the principal components that maximise a robust dispersion measure. We also explain the need to use a dispersion functional with a continuous influence function.en_HK
dc.languageengen_HK
dc.publisherOxford University Press. The Journal's web site is located at http://biomet.oxfordjournals.org/en_HK
dc.relation.ispartofBiometrikaen_HK
dc.rightsBiometrika. Copyright © Oxford University Press.en_HK
dc.subjectAsymptotic normalityen_HK
dc.subjectDispersionen_HK
dc.subjectPrincipal componenten_HK
dc.subjectProjection pursuiten_HK
dc.subjectRobustnessen_HK
dc.titleAsymptotic distributions of principal components based on robust dispersionsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0006-3444&volume=90&issue=4&spage=953&epage=966&date=2003&atitle=Asymptotic+distributions+of+principal+components+based+on+robust+dispersionsen_HK
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_HK
dc.identifier.authorityNg, KW=rp00765en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1093/biomet/90.4.953en_HK
dc.identifier.scopuseid_2-s2.0-3843068589en_HK
dc.identifier.hkuros85216en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-3843068589&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume90en_HK
dc.identifier.issue4en_HK
dc.identifier.spage953en_HK
dc.identifier.epage966en_HK
dc.identifier.isiWOS:000187321500015-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridCui, H=7201385510en_HK
dc.identifier.scopusauthoridHe, X=7404407842en_HK
dc.identifier.scopusauthoridNg, KW=7403178774en_HK

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