Before revision:  Under weak assumptions, the estimator of the functional concentrates in a L/\sqrt{n Our analysis yields weak `` double sparsity robustness '' : either the approximation to the regression or the approximation to the representer can be ``completely dense'' as long as the other is sufficiently ``sparse'' . Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.
After revision:  Under weak assumptions, the estimator of the functional concentrates in a L/\sqrt{n Our analysis yields weak " double sparsity robustness '' : either the approximation to the regression or the approximation to the representer can be ``completely dense'' as long as the other is sufficiently ``sparse'' . Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.