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August 2009 Simultaneous analysis of Lasso and Dantzig selector
Peter J. Bickel, Ya’acov Ritov, Alexandre B. Tsybakov
Ann. Statist. 37(4): 1705-1732 (August 2009). DOI: 10.1214/08-AOS620

Abstract

We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. For both methods, we derive, in parallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the p estimation loss for 1≤p≤2 in the linear model when the number of variables can be much larger than the sample size.

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Peter J. Bickel. Ya’acov Ritov. Alexandre B. Tsybakov. "Simultaneous analysis of Lasso and Dantzig selector." Ann. Statist. 37 (4) 1705 - 1732, August 2009. https://doi.org/10.1214/08-AOS620

Information

Published: August 2009
First available in Project Euclid: 18 June 2009

zbMATH: 1173.62022
MathSciNet: MR2533469
Digital Object Identifier: 10.1214/08-AOS620

Subjects:
Primary: 60K35, 62G08
Secondary: 62C20, 62G05, 62G20

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 4 • August 2009
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