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Article: An overview of asymptotic properties of Lp regression under general classes of error distributions

TitleAn overview of asymptotic properties of Lp regression under general classes of error distributions
Authors
KeywordsConvergence rate
Gaussian process
Lp estimator
M out of n bootstrap
Regression
Issue Date2005
PublisherAmerican Statistical Association. The Journal's web site is located at http://www.amstat.org/publications/jasa/index.cfm?fuseaction=main
Citation
Journal Of The American Statistical Association, 2005, v. 100 n. 470, p. 446-458 How to Cite?
AbstractWe survey the asymptotic properties of regression Lp estimators under general classes of error distributions. It is found that the asymptotic distributions of Lp estimators depend crucially on p and the shape of the error distribution near the origin. A number of important features arise as a result, among which are (a) use of a small p may yield accelerated convergence rates for Lp estimators under certain classes of error distributions; (b) for p < 1, Lp regression should, under some circumstances, be undertaken by locally maximizing, rather than minimizing, the sum of the pth powers of the absolute deviations; and (c) consistent estimation of the sampling distributions of the Lp estimators can be achieved by the m out of n bootstrap in general. Numerical examples are provided to illustrate our theoretical findings, and a computational algorithm is suggested for local maximization as may sometimes be required by the Lp procedure. © 2005 American Statistical Association.
Persistent Identifierhttp://hdl.handle.net/10722/82748
ISSN
2015 Impact Factor: 1.725
2015 SCImago Journal Rankings: 3.447
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLai, PYen_HK
dc.contributor.authorLee, SMSen_HK
dc.date.accessioned2010-09-06T08:32:58Z-
dc.date.available2010-09-06T08:32:58Z-
dc.date.issued2005en_HK
dc.identifier.citationJournal Of The American Statistical Association, 2005, v. 100 n. 470, p. 446-458en_HK
dc.identifier.issn0162-1459en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82748-
dc.description.abstractWe survey the asymptotic properties of regression Lp estimators under general classes of error distributions. It is found that the asymptotic distributions of Lp estimators depend crucially on p and the shape of the error distribution near the origin. A number of important features arise as a result, among which are (a) use of a small p may yield accelerated convergence rates for Lp estimators under certain classes of error distributions; (b) for p < 1, Lp regression should, under some circumstances, be undertaken by locally maximizing, rather than minimizing, the sum of the pth powers of the absolute deviations; and (c) consistent estimation of the sampling distributions of the Lp estimators can be achieved by the m out of n bootstrap in general. Numerical examples are provided to illustrate our theoretical findings, and a computational algorithm is suggested for local maximization as may sometimes be required by the Lp procedure. © 2005 American Statistical Association.en_HK
dc.languageengen_HK
dc.publisherAmerican Statistical Association. The Journal's web site is located at http://www.amstat.org/publications/jasa/index.cfm?fuseaction=mainen_HK
dc.relation.ispartofJournal of the American Statistical Associationen_HK
dc.subjectConvergence rateen_HK
dc.subjectGaussian processen_HK
dc.subjectLp estimatoren_HK
dc.subjectM out of n bootstrapen_HK
dc.subjectRegressionen_HK
dc.titleAn overview of asymptotic properties of Lp regression under general classes of error distributionsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0162-1459&volume=100&spage=446&epage=458&date=2005&atitle=An+overview+of+asymptotic+properties+of+Lp+regression+under+general+classes+of+error+distributionsen_HK
dc.identifier.emailLee, SMS: smslee@hku.hken_HK
dc.identifier.authorityLee, SMS=rp00726en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1198/016214504000001385en_HK
dc.identifier.scopuseid_2-s2.0-20444475020en_HK
dc.identifier.hkuros100412en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-20444475020&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume100en_HK
dc.identifier.issue470en_HK
dc.identifier.spage446en_HK
dc.identifier.epage458en_HK
dc.identifier.isiWOS:000233311300008-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridLai, PY=8629588700en_HK
dc.identifier.scopusauthoridLee, SMS=24280225500en_HK
dc.identifier.citeulike207477-

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