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2008 Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
Karim Lounici
Electron. J. Statist. 2: 90-102 (2008). DOI: 10.1214/08-EJS177

Abstract

We derive the l convergence rate simultaneously for Lasso and Dantzig estimators in a high-dimensional linear regression model under a mutual coherence assumption on the Gram matrix of the design and two different assumptions on the noise: Gaussian noise and general noise with finite variance. Then we prove that simultaneously the thresholded Lasso and Dantzig estimators with a proper choice of the threshold enjoy a sign concentration property provided that the non-zero components of the target vector are not too small.

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Karim Lounici. "Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators." Electron. J. Statist. 2 90 - 102, 2008. https://doi.org/10.1214/08-EJS177

Information

Published: 2008
First available in Project Euclid: 12 February 2008

zbMATH: 1306.62155
MathSciNet: MR2386087
Digital Object Identifier: 10.1214/08-EJS177

Subjects:
Primary: 62J05
Secondary: 62F12

Keywords: Dantzig , Lasso , linear model , Model selection , sign consistency , Sparsity

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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