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Article: An adaptive estimation of dimension reduction space

TitleAn adaptive estimation of dimension reduction space
Authors
KeywordsAverage Derivative Estimation
Dimension Reduction
Generalized Linear Models
Local Linear Smoother
Multiple Time Series
Non-Linear Time Series Analysis
Nonparametric Regression
Principal Hessian Direction
Projection Pursuit
Semiparametrics
Issue Date2002
PublisherWiley-Blackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/RSSB
Citation
Journal Of The Royal Statistical Society. Series B: Statistical Methodology, 2002, v. 64 n. 3, p. 363-388 How to Cite?
AbstractSearching for an effective dimension reduction space is an important problem in regression, especially for high dimensional data. We propose an adaptive approach based on semiparametric models, which we call the (conditional) minimum average variance estimation (MAVE) method, within quite a general setting. The MAVE method has the following advantages. Most existing methods must undersmooth the nonparametric link function estimator to achieve a faster rate of consistency for the estimator of the parameters (than for that of the nonparametric function). In contrast, a faster consistency rate can be achieved by the MAVE method even without undersmoothing the nonparametric link function estimator. The MAVE method is applicable to a wide range of models, with fewer restrictions on the distribution of the covariates, to the extent that even time series can be included. Because of the faster rate of consistency for the parameter estimators, it is possible for us to estimate the dimension of the space consistently. The relationship of the MAVE method with other methods is also investigated. In particular, a simple outer product gradient estimator is proposed as an initial estimator. In addition to theoretical results, we demonstrate the efficacy of the MAVE method for high dimensional data sets through simulation. Two real data sets are analysed by using the MAVE approach.
Persistent Identifierhttp://hdl.handle.net/10722/172390
ISSN
2015 Impact Factor: 4.222
2015 SCImago Journal Rankings: 7.429
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorXia, Yen_US
dc.contributor.authorTong, Hen_US
dc.contributor.authorLi, WKen_US
dc.contributor.authorZhu, LXen_US
dc.date.accessioned2012-10-30T06:22:18Z-
dc.date.available2012-10-30T06:22:18Z-
dc.date.issued2002en_US
dc.identifier.citationJournal Of The Royal Statistical Society. Series B: Statistical Methodology, 2002, v. 64 n. 3, p. 363-388en_US
dc.identifier.issn1369-7412en_US
dc.identifier.urihttp://hdl.handle.net/10722/172390-
dc.description.abstractSearching for an effective dimension reduction space is an important problem in regression, especially for high dimensional data. We propose an adaptive approach based on semiparametric models, which we call the (conditional) minimum average variance estimation (MAVE) method, within quite a general setting. The MAVE method has the following advantages. Most existing methods must undersmooth the nonparametric link function estimator to achieve a faster rate of consistency for the estimator of the parameters (than for that of the nonparametric function). In contrast, a faster consistency rate can be achieved by the MAVE method even without undersmoothing the nonparametric link function estimator. The MAVE method is applicable to a wide range of models, with fewer restrictions on the distribution of the covariates, to the extent that even time series can be included. Because of the faster rate of consistency for the parameter estimators, it is possible for us to estimate the dimension of the space consistently. The relationship of the MAVE method with other methods is also investigated. In particular, a simple outer product gradient estimator is proposed as an initial estimator. In addition to theoretical results, we demonstrate the efficacy of the MAVE method for high dimensional data sets through simulation. Two real data sets are analysed by using the MAVE approach.en_US
dc.languageengen_US
dc.publisherWiley-Blackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/RSSBen_US
dc.relation.ispartofJournal of the Royal Statistical Society. Series B: Statistical Methodologyen_US
dc.subjectAverage Derivative Estimationen_US
dc.subjectDimension Reductionen_US
dc.subjectGeneralized Linear Modelsen_US
dc.subjectLocal Linear Smootheren_US
dc.subjectMultiple Time Seriesen_US
dc.subjectNon-Linear Time Series Analysisen_US
dc.subjectNonparametric Regressionen_US
dc.subjectPrincipal Hessian Directionen_US
dc.subjectProjection Pursuiten_US
dc.subjectSemiparametricsen_US
dc.titleAn adaptive estimation of dimension reduction spaceen_US
dc.typeArticleen_US
dc.identifier.emailLi, WK: hrntlwk@hku.hken_US
dc.identifier.authorityLi, WK=rp00741en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1111/1467-9868.03412-
dc.identifier.scopuseid_2-s2.0-0036428498en_US
dc.identifier.hkuros72704-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0036428498&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume64en_US
dc.identifier.issue3en_US
dc.identifier.spage363en_US
dc.identifier.epage388en_US
dc.identifier.isiWOS:000177425500003-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridXia, Y=7403027730en_US
dc.identifier.scopusauthoridTong, H=7201359749en_US
dc.identifier.scopusauthoridLi, WK=14015971200en_US
dc.identifier.scopusauthoridZhu, LX=7404201068en_US

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