Simultaneous analysis of lasso and dantzig selector

Peter J. Bickel; Ya'acov Ritov; Alexandre B. Tsybakov

doi:10.1214/08-AOS620

Simultaneous analysis of lasso and dantzig selector

Peter J. Bickel
, Ya'acov Ritov
, Alexandre B. Tsybakov

Research output: Contribution to journal › Article › peer-review

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

Original language	English
Pages (from-to)	1705-1732
Number of pages	28
Journal	Annals of Statistics
Volume	37
Issue number	4
DOIs	https://doi.org/10.1214/08-AOS620
Publication status	Published - 1 Aug 2009
Externally published	Yes

Keywords

Linear models
Model selection
Nonparametric statistics

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10.1214/08-AOS620

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title = "Simultaneous analysis of lasso and dantzig selector",

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 ℓp 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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year = "2009",

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AU - Ritov, Ya'acov

AU - Tsybakov, Alexandre B.

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

KW - Linear models

KW - Model selection

KW - Nonparametric statistics

UR - https://www.scopus.com/pages/publications/68649086910

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DO - 10.1214/08-AOS620

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Simultaneous analysis of lasso and dantzig selector

Abstract

Keywords

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