Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators. (English) Zbl 1306.62155

Summary: 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.


62J05 Linear regression; mixed models
62F12 Asymptotic properties of parametric estimators


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