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

Karim Lounici (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Linear model; Lasso; Dantzig; Sparsity; Model selection; Sign consistency

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

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