High-dimensional stochastic optimization with the generalized Dantzig estimator

Details High-dimensional stochastic optimization with the generalized Dantzig estimator High-dimensional stochastic optimization with the generalized Dantzig estimator

2008-11-14

arxiv.org/abs/0811.2281v1

Mathematics

Statistics Theory

Scientific paper

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.

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