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arXiv · 0801.1095

Simultaneous analysis of Lasso and Dantzig selector

Peter J. Bickel·Ya'acov Ritov·Alexandre B. Tsybakov
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Abstract

We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the $\ell_p$ estimation loss for $1\le p\le 2$ 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. 2008-01-07. Simultaneous analysis of Lasso and Dantzig selector. https://doi.org/10.1214/08-aos620

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