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dc.contributor.authorWang, Lie
dc.date.accessioned2015-10-26T16:06:25Z
dc.date.available2015-10-26T16:06:25Z
dc.date.issued2013-04
dc.date.submitted2012-05
dc.identifier.issn0047259X
dc.identifier.issn1095-7243
dc.identifier.urihttp://hdl.handle.net/1721.1/99451
dc.description.abstractIn this paper, the high-dimensional sparse linear regression model is considered, where the overall number of variables is larger than the number of observations. We investigate the L[subscript 1] penalized least absolute deviation method. Different from most of the other methods, the L[subscript 1] penalized LAD method does not need any knowledge of standard deviation of the noises or any moment assumptions of the noises. Our analysis shows that the method achieves near oracle performance, i.e. with large probability, the L[subscript 2] norm of the estimation error is of order View the O(√k log p/n). The result is true for a wide range of noise distributions, even for the Cauchy distribution. Numerical results are also presented.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant DMS-1005539)en_US
dc.language.isoen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.jmva.2013.04.001en_US
dc.rightsCreative Commons Attribution-Noncommercial-NoDerivativesen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.sourceMIT Web Domainen_US
dc.titleThe L[subscript 1] penalized LAD estimator for high dimensional linear regressionen_US
dc.typeArticleen_US
dc.identifier.citationWang, Lie. “The L[subscript 1] Penalized LAD Estimator for High Dimensional Linear Regression.” Journal of Multivariate Analysis 120 (September 2013): 135–151.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorWang, Lieen_US
dc.relation.journalJournal of Multivariate Analysisen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsWang, Lieen_US
dc.identifier.orcidhttps://orcid.org/0000-0003-3582-8898
mit.licensePUBLISHER_CCen_US
mit.metadata.statusComplete


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