The L[subscript 1] penalized LAD estimator for high dimensional linear regression
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Wang_L1 penalized.pdf
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174.44 KB
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5212e8ef30c208bb037687a217968969
Author(s)
Wang, Lie
Date Issued
April 2013
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-NoDerivatives
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DOI of Published Version
https://doi.org/10.1016/j.jmva.2013.04.001
