The paper by Bickel, Ritov, and Tsybakov compares the Lasso and Dantzig selector estimators under a sparsity scenario. Both methods are shown to exhibit similar behavior in terms of prediction risk and $\ell_p$ estimation loss for $1 \leq p \leq 2$ in both linear and nonparametric regression models. The authors derive oracle inequalities for the prediction risk in the general nonparametric regression model and bounds on the $\ell_p$ estimation loss for the linear model when the number of variables can be much larger than the sample size. The results are non-asymptotic and cover both linear and nonparametric regression models. The paper also introduces geometric assumptions that are weaker than those used in previous studies, and discusses their implications for the Lasso and Dantzig selector.The paper by Bickel, Ritov, and Tsybakov compares the Lasso and Dantzig selector estimators under a sparsity scenario. Both methods are shown to exhibit similar behavior in terms of prediction risk and $\ell_p$ estimation loss for $1 \leq p \leq 2$ in both linear and nonparametric regression models. The authors derive oracle inequalities for the prediction risk in the general nonparametric regression model and bounds on the $\ell_p$ estimation loss for the linear model when the number of variables can be much larger than the sample size. The results are non-asymptotic and cover both linear and nonparametric regression models. The paper also introduces geometric assumptions that are weaker than those used in previous studies, and discusses their implications for the Lasso and Dantzig selector.