On cross-validated Lasso in high dimensions

In this paper, we derive nonasymptotic error bounds for the Lasso estimator when penalty parameter is chosen using K-fold cross-validation. Our imply that cross-validated has nearly optimal rates of convergence in prediction, L2, and L1 norms. For example, show model with Gaussian noise under fairly general assumptions on candidate set values parameter, estimation converges to zero prediction norm slogp/n×log(pn) rate, where n sample size available data, p number covariates s nonzero coefficients model. Thus, achieves fastest possible rate up a small logarithmic factor log(pn), similar conclusions apply both L2 Importantly, our results cover case (potentially much) larger than also allow non-Gaussian noise. paper therefore serves as justification widely spread practice cross-validation method choose estimator.