Simultaneous analysis of lasso and dantzig selector

  • Bickel P
  • Ritov Y
  • Tsybakov A
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Abstract

We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. For both methods, we derive, in par-allel, 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.

Author-supplied keywords

  • Linear models
  • Model selection
  • Nonparametric statistics

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Authors

  • Peter J. Bickel

  • Ya'acov Ritov

  • Alexandre B. Tsybakov

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