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June 18, 2009Open Access

Simultaneous analysis of Lasso and Dantzig selector

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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 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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Authors

Peter J. Bickel

University of Stuttgart

Ya’acov Ritov

University of Michigan

Alexandre B. Tsybakov

Florida State University

Journals

The Annals of Statistics

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Institutions

University of California, Berkeley

Sorbonne Université

Hebrew University of Jerusalem

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Bickel et al. (Thu,) studied this question.

synapsesocial.com/papers/6a09baa316dfdfe7ed345399 — DOI: https://doi.org/10.1214/08-aos620

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Sparsity oracle inequalities for the Lasso· 2012 · 421 citations
The sparsity and bias of the Lasso selection in high-dimensional linear regression· 2008 · 500 citations
Regression Shrinkage and Selection Via the Lasso· 1996 · 51,639 citations
The Dantzig selector: Statistical estimation when $p$ is much larger than $n$· 2005 · 1,725 citations
On Model Selection Consistency of Lasso· 2006 · 1,028 citations

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Sparsity oracle inequalities for the Lasso· 2012 · 421 citations
The sparsity and bias of the Lasso selection in high-dimensional linear regression· 2008 · 500 citations
Regression Shrinkage and Selection Via the Lasso· 1996 · 51,639 citations
The Dantzig selector: Statistical estimation when $p$ is much larger than $n$· 2005 · 1,725 citations
On Model Selection Consistency of Lasso· 2006 · 1,028 citations

Simultaneous analysis of Lasso and Dantzig selector

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Abstract

Citation Network

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Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study

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