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

University of California, Berkeley
The Hebrew University of Jerusalem
ENSAE
Laboratoire de Probabilités, Statistique et Modélisation

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

1650 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	1705-1732
Nombre de pages	28
journal	Annals of Statistics
Volume	37
Numéro de publication	4
Les DOIs	https://doi.org/10.1214/08-AOS620
état	Publié - 1 août 2009
Modification externe	Oui

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10.1214/08-AOS620

Contient cette citation

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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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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

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DO - 10.1214/08-AOS620

M3 - Article

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JO - Annals of Statistics

JF - Annals of Statistics

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Simultaneous analysis of lasso and dantzig selector

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