Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 120, Issue -, Pages 135-151Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2013.04.001
Keywords
High dimensional regression; LAD estimator; L-1 penalization; Variable selection
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Funding
- NSF [DMS-1005539]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1005539] Funding Source: National Science Foundation
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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-1 penalized least absolute deviation method. Different from most of the other methods, the L-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-2 norm of the estimation error is of order O(root 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. (C) 2013 Elsevier Inc. All rights reserved.
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