Before revision:  TAlasso's penalty scheme accommodates the system of heterogeneous regressors, and it recovers the well-known oracle property that implies variable selection consistency and optimal rate of convergence for all three types of regressors. On the contrary , conventional LASSO fails to attain coefficient estimation consistency and variable screening in all components simultaneously , since its penalty is imposed according to the marginal behavior of each individual regressor only.
After revision:  TAlasso's penalty scheme accommodates the system of heterogeneous regressors, and it recovers the well-known oracle property . In contrast , conventional LASSO fails to attain coefficient estimation consistency and variable screening in all components simultaneously , since its penalty is imposed according to the marginal behavior of each individual regressor only.