MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

The L[subscript 1] penalized LAD estimator for high dimensional linear regression

Author(s)
Wang, Lie
Thumbnail
DownloadWang_L1 penalized.pdf (174.4Kb)
PUBLISHER_CC

Publisher with Creative Commons License

Creative Commons Attribution

Terms of use
Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/
Metadata
Show full item record
Abstract
In 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.
Date issued
2013-04
URI
http://hdl.handle.net/1721.1/99451
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Multivariate Analysis
Publisher
Elsevier
Citation
Wang, Lie. “The L[subscript 1] Penalized LAD Estimator for High Dimensional Linear Regression.” Journal of Multivariate Analysis 120 (September 2013): 135–151.
Version: Author's final manuscript
ISSN
0047259X
1095-7243

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.