The L1 penalized LAD estimator for high dimensional linear regression

Lie Wang

Journal of Multivariate Analysis, 2013, vol. 120, issue C, 135-151

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 L1 penalized least absolute deviation method. Different from most of the other methods, the L1 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 L2 norm of the estimation error is of order O(klogp/n). The result is true for a wide range of noise distributions, even for the Cauchy distribution. Numerical results are also presented.

Keywords: High dimensional regression; LAD estimator; L1 penalization; Variable selection (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (31)

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DOI: 10.1016/j.jmva.2013.04.001

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