We establish estimation and model selection consistency, prediction and estimation bounds and persistence for the group-lasso estimator and model selector proposed by Yuan and Lin (2006) for least squares problems when the covariates have a natural grouping structure. We consider the case of a fixed-dimensional parameter space with increasing sample size and the double asymptotic scenario where the model complexity changes with the sample size.
"On the asymptotic properties of the group lasso estimator for linear models." Electron. J. Statist. 2 605 - 633, 2008. https://doi.org/10.1214/08-EJS200