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Robust Lasso Regression Using Tukey's Biweight Criterion

Chang, Le; Roberts, Steven; Welsh, Alan

Description

The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that the adaptive lasso achieves the oracle property. In this work, we propose an extension of the adaptive lasso named the Tukey-lasso. By using Tukey's biweight criterion, instead of squared loss, the Tukey-lasso is resistant to outliers in both the response and covariates. Importantly, we demonstrate that the Tukey-lasso also enjoys the...[Show more]

dc.contributor.authorChang, Le
dc.contributor.authorRoberts, Steven
dc.contributor.authorWelsh, Alan
dc.date.accessioned2020-12-20T20:50:25Z
dc.date.available2020-12-20T20:50:25Z
dc.identifier.issn0040-1706
dc.identifier.urihttp://hdl.handle.net/1885/217443
dc.description.abstractThe adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that the adaptive lasso achieves the oracle property. In this work, we propose an extension of the adaptive lasso named the Tukey-lasso. By using Tukey's biweight criterion, instead of squared loss, the Tukey-lasso is resistant to outliers in both the response and covariates. Importantly, we demonstrate that the Tukey-lasso also enjoys the oracle property. A fast accelerated proximal gradient (APG) algorithm is proposed and implemented for computing the Tukey-lasso. Our extensive simulations show that the Tukey-lasso, implemented with the APG algorithm, achieves very reliable results, including for high-dimensional data where p > n. In the presence of outliers, the Tukey-lasso is shown to offer substantial improvements in performance compared to the adaptive lasso and other robust implementations of the lasso. Real-data examples further demonstrate the utility of the Tukey-lasso. Supplementary materials for this article are available online.
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherAmerican Statistical Association
dc.rightsPlease, fill new ANU author/investigator form for Le Chang. https://services.anu.edu.au/webform/aries-new-investigator-or-author-registration
dc.sourceTechnometrics
dc.titleRobust Lasso Regression Using Tukey's Biweight Criterion
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume60
dc.date.issued2017
local.identifier.absfor010401 - Applied Statistics
local.identifier.ariespublicationa383154xPUB7483
local.type.statusMetadata only
local.contributor.affiliationChang, Le, College of Business and Economics, ANU
local.contributor.affiliationRoberts, Steven, College of Business and Economics, ANU
local.contributor.affiliationWelsh, Alan, College of Science, ANU
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage36
local.bibliographicCitation.lastpage47
local.identifier.doi10.1080/00401706.2017.1305299
dc.date.updated2020-11-02T04:18:34Z
local.identifier.scopusID2-s2.0-85024481206
CollectionsANU Research Publications

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