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Article: Simultaneous estimation and variable selection in median regression using Lasso-type penalty

TitleSimultaneous estimation and variable selection in median regression using Lasso-type penalty
Authors
KeywordsVariable selection
Median regression
Least absolute deviations
Lasso
Perturbation
Bayesian information criterion
Issue Date2010
Citation
Annals of the Institute of Statistical Mathematics, 2010, v. 62, n. 3, p. 487-514 How to Cite?
AbstractWe consider the median regression with a LASSO-type penalty term for variable selection. With the fixed number of variables in regression model, a two-stage method is proposed for simultaneous estimation and variable selection where the degree of penalty is adaptively chosen. A Bayesian information criterion type approach is proposed and used to obtain a data-driven procedure which is proved to automatically select asymptotically optimal tuning parameters. It is shown that the resultant estimator achieves the so-called oracle property. The combination of the median regression and LASSO penalty is computationally easy to implement via the standard linear programming. A random perturbation scheme can be made use of to get simple estimator of the standard error. Simulation studies are conducted to assess the finite-sample performance of the proposed method. We illustrate the methodology with a real example.
Persistent Identifierhttp://hdl.handle.net/10722/221682
ISSN
2015 Impact Factor: 0.768
2015 SCImago Journal Rankings: 0.931
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorXu, J-
dc.contributor.authorYing, Z-
dc.date.accessioned2015-12-04T15:29:04Z-
dc.date.available2015-12-04T15:29:04Z-
dc.date.issued2010-
dc.identifier.citationAnnals of the Institute of Statistical Mathematics, 2010, v. 62, n. 3, p. 487-514-
dc.identifier.issn0020-3157-
dc.identifier.urihttp://hdl.handle.net/10722/221682-
dc.description.abstractWe consider the median regression with a LASSO-type penalty term for variable selection. With the fixed number of variables in regression model, a two-stage method is proposed for simultaneous estimation and variable selection where the degree of penalty is adaptively chosen. A Bayesian information criterion type approach is proposed and used to obtain a data-driven procedure which is proved to automatically select asymptotically optimal tuning parameters. It is shown that the resultant estimator achieves the so-called oracle property. The combination of the median regression and LASSO penalty is computationally easy to implement via the standard linear programming. A random perturbation scheme can be made use of to get simple estimator of the standard error. Simulation studies are conducted to assess the finite-sample performance of the proposed method. We illustrate the methodology with a real example.-
dc.languageeng-
dc.relation.ispartofAnnals of the Institute of Statistical Mathematics-
dc.subjectVariable selection-
dc.subjectMedian regression-
dc.subjectLeast absolute deviations-
dc.subjectLasso-
dc.subjectPerturbation-
dc.subjectBayesian information criterion-
dc.titleSimultaneous estimation and variable selection in median regression using Lasso-type penalty-
dc.typeArticle-
dc.identifier.emailXu, J: xujf@hku.hk-
dc.identifier.authorityXu, J=rp02086-
dc.identifier.doi10.1007/s10463-008-0184-2-
dc.identifier.scopuseid_2-s2.0-77950692172-
dc.identifier.volume62-
dc.identifier.spage487-
dc.identifier.epage514-
dc.identifier.isiWOS:000276161700004-

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