# Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators

Abstract : We derive $l_{\infty}$ 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00222251
Contributor : Karim Lounici <>
Submitted on : Tuesday, January 29, 2008 - 12:26:30 PM
Last modification on : Sunday, March 31, 2019 - 1:41:45 AM
Long-term archiving on : Friday, April 30, 2010 - 1:11:18 AM

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lounici.pdf
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• HAL Id : hal-00222251, version 1

### Citation

Karim Lounici. Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators. 2008. ⟨hal-00222251⟩

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