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

2008/01/01 by Karim Lounici · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Random Matrices and Applications #Statistical Methods and Inference #math.ST #msc:62F12 #msc:62J05 #stat.TH

paper · pdf · doi:10.1214/08-ejs177

published as Electronic Journal of Statistics 2008, Vol. 2, 90-102 · Published in at http://dx.doi.org/10.1214/08-EJS177 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2008/01/01 · arxiv created 2008/02/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Atomic Decomposition by Basis Pursuit
• Least angle regression

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