The L[subscript 1] penalized LAD estimator for high dimensional linear regression
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]...
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| Format: | Article |
| Language: | en_US |
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Elsevier
2015
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| Online Access: | http://hdl.handle.net/1721.1/99451 https://orcid.org/0000-0003-3582-8898 |
| _version_ | 1826199401550315520 |
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| author | Wang, Lie |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Wang, Lie |
| author_sort | Wang, Lie |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:19:38Z |
| format | Article |
| id | mit-1721.1/99451 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:19:38Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/994512022-09-27T18:43:09Z The L[subscript 1] penalized LAD estimator for high dimensional linear regression Wang, Lie Massachusetts Institute of Technology. Department of Mathematics Wang, Lie 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. National Science Foundation (U.S.) (Grant DMS-1005539) 2015-10-26T16:06:25Z 2015-10-26T16:06:25Z 2013-04 2012-05 Article http://purl.org/eprint/type/JournalArticle 0047259X 1095-7243 http://hdl.handle.net/1721.1/99451 Wang, Lie. “The L[subscript 1] Penalized LAD Estimator for High Dimensional Linear Regression.” Journal of Multivariate Analysis 120 (September 2013): 135–151. https://orcid.org/0000-0003-3582-8898 en_US http://dx.doi.org/10.1016/j.jmva.2013.04.001 Journal of Multivariate Analysis Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier MIT Web Domain |
| spellingShingle | Wang, Lie The L[subscript 1] penalized LAD estimator for high dimensional linear regression |
| title | The L[subscript 1] penalized LAD estimator for high dimensional linear regression |
| title_full | The L[subscript 1] penalized LAD estimator for high dimensional linear regression |
| title_fullStr | The L[subscript 1] penalized LAD estimator for high dimensional linear regression |
| title_full_unstemmed | The L[subscript 1] penalized LAD estimator for high dimensional linear regression |
| title_short | The L[subscript 1] penalized LAD estimator for high dimensional linear regression |
| title_sort | l subscript 1 penalized lad estimator for high dimensional linear regression |
| url | http://hdl.handle.net/1721.1/99451 https://orcid.org/0000-0003-3582-8898 |
| work_keys_str_mv | AT wanglie thelsubscript1penalizedladestimatorforhighdimensionallinearregression AT wanglie lsubscript1penalizedladestimatorforhighdimensionallinearregression |