Some theoretical results on the grouped variables Lasso
Résumé
We consider the linear regression model with Gaussian error. We estimate the unknown parameters by a procedure inspired from the Group Lasso estimator introduced by Yuan and Lin (2006). We show that this estimator satisfies a sparsity oracle inequality, i.e., a bound in terms of the number of non-zero components of the oracle vector. We prove that this bound is better, in some cases, than the one achieved by the Lasso and the Dantzig selector.
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