High-dimensional stochastic optimization with the generalized Dantzig estimator

Karim Lounici (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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 of high-dimensional linear regression model selection with the Huber loss function. In this case we derive the sup-norm convergence rate and the sign concentration property of the Dantzig estimators under a mutual coherence assumption on the dictionary.

Mots clés: Dantzig; Sparsity; Prediction; Estimation; Sign consistency

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

Karim Lounici. High-dimensional stochastic optimization with the generalized Dantzig estimator. 2008. ⟨hal-00338663⟩