In this paper, we derive a rate of convergence of the Lasso estimator when the penalty parameter Lambda for the …-validated Lasso estimator is with high probability bounded from above up-to a constant by (s log p/n)1/2 . (log7/8 n) as long as p log … sparsity bound for the cross-validated Lasso estimator; in particular, we show that under the same conditions as above, the …