  We derive the $l_{\infty}$ 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.
