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.
Finally, Lounici REF studied the ∞ error convergence rate for Lasso and Dantzig estimators.
Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
Electronic Journal of Statistics 2008, Vol. 2, 90-102
Mathematics