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math.ST2008★ 4 cited
High-dimensional stochastic optimization with the generalized Dantzig estimator
Karim Lounici
We propose a generalized version of the Dantzig selector. We show that it satisfies sparsity oracle inequalities in prediction and estimation. We consider then the particular case…
math.ST2008★ 119 cited
Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
Karim Lounici
We derive the convergence rate simultaneously for Lasso and Dantzig estimators in a high-dimensional linear regression model under a mutual coherence assumption on the…