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SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR (2007)

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by Peter J. Bickel , Alexandre Tsybakov, et al.
Venue:SUBMITTED TO THE ANNALS OF STATISTICS
Citations:471 - 11 self
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BibTeX

@MISC{Bickel07simultaneousanalysis,
    author = {Peter J. Bickel and Alexandre Tsybakov and et al.},
    title = {SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR },
    year = {2007}
}

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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 ℓp estimation loss for 1 ≤ p ≤ 2 in the linear model when the number of variables can be much larger than the sample size.

Keyphrases

simultaneous analysis lasso dantzig selector    linear model    sample size    general nonparametric regression model    prediction risk    parallel oracle inequality    approximate equivalence    lasso estimator    dantzig selector    estimation loss   

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