High-dimensional stochastic optimization with the generalized Dantzig estimator
Statistics Theory
2008-11-17 v1 Statistics Theory
Abstract
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.
Cite
@article{arxiv.0811.2281,
title = {High-dimensional stochastic optimization with the generalized Dantzig estimator},
author = {Karim Lounici},
journal= {arXiv preprint arXiv:0811.2281},
year = {2008}
}