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Article: Dimension reduction based on canonical correlation

TitleDimension reduction based on canonical correlation
Authors
KeywordsAsymptotic distribution
Canonical correlation
Dimension reduction
Mixing
Sliced inverse regression
Splines
Issue Date2002
PublisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/
Citation
Statistica Sinica, 2002, v. 12 n. 4, p. 1093-1113 How to Cite?
AbstractDimension reduction is helpful and often necessary in exploring nonlinear or nonparametric regression structures with a large number of predictors. We consider using the canonical variables from the design space whose correlations with a spline basis in the response space are significant. The method can be viewed as a variant of sliced inverse regression (SIR) with simple slicing replaced by B-spline basis functions. The asymptotic distribution theory we develop extends to weakly dependent stationary sequences and enables us to consider asymptotic tests that are useful in determining the number of significant dimensions for modeling. We compare several tests for dimensionality and make specific recommendations for dimension selection based on our theoretical and empirical studies. These tests apply to any form of SIR. The methodology and some of the practical issues are illustrated through a tuition study of American colleges.
Persistent Identifierhttp://hdl.handle.net/10722/45357
ISSN
2015 Impact Factor: 0.838
2015 SCImago Journal Rankings: 2.292
References

 

DC FieldValueLanguage
dc.contributor.authorFung, WKen_HK
dc.contributor.authorHe, Xen_HK
dc.contributor.authorLiu, Len_HK
dc.contributor.authorShi, Pen_HK
dc.date.accessioned2007-10-30T06:23:41Z-
dc.date.available2007-10-30T06:23:41Z-
dc.date.issued2002en_HK
dc.identifier.citationStatistica Sinica, 2002, v. 12 n. 4, p. 1093-1113en_HK
dc.identifier.issn1017-0405en_HK
dc.identifier.urihttp://hdl.handle.net/10722/45357-
dc.description.abstractDimension reduction is helpful and often necessary in exploring nonlinear or nonparametric regression structures with a large number of predictors. We consider using the canonical variables from the design space whose correlations with a spline basis in the response space are significant. The method can be viewed as a variant of sliced inverse regression (SIR) with simple slicing replaced by B-spline basis functions. The asymptotic distribution theory we develop extends to weakly dependent stationary sequences and enables us to consider asymptotic tests that are useful in determining the number of significant dimensions for modeling. We compare several tests for dimensionality and make specific recommendations for dimension selection based on our theoretical and empirical studies. These tests apply to any form of SIR. The methodology and some of the practical issues are illustrated through a tuition study of American colleges.en_HK
dc.format.extent244066 bytes-
dc.format.extent1982 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/en_HK
dc.relation.ispartofStatistica Sinicaen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectAsymptotic distributionen_HK
dc.subjectCanonical correlationen_HK
dc.subjectDimension reductionen_HK
dc.subjectMixingen_HK
dc.subjectSliced inverse regressionen_HK
dc.subjectSplinesen_HK
dc.titleDimension reduction based on canonical correlationen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1017-0405&volume=12&issue=4&spage=1093&epage=1113&date=2002&atitle=Dimension+reduction+based+on+canonical+correlationen_HK
dc.identifier.emailFung, WK: wingfung@hku.hken_HK
dc.identifier.authorityFung, WK=rp00696en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.scopuseid_2-s2.0-0036822251en_HK
dc.identifier.hkuros80136-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0036822251&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume12en_HK
dc.identifier.issue4en_HK
dc.identifier.spage1093en_HK
dc.identifier.epage1113en_HK
dc.publisher.placeTaiwan, Republic of Chinaen_HK
dc.identifier.scopusauthoridFung, WK=13310399400en_HK
dc.identifier.scopusauthoridHe, X=7404407842en_HK
dc.identifier.scopusauthoridLiu, L=36068379000en_HK
dc.identifier.scopusauthoridShi, P=7202161006en_HK

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