Before revision:  This new finding motivates a simple but novel post-selection adaptive LASSO, which we call the twin adaptive LASSO (TAlasso), to fix variable selection inconsistency. 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.
After revision:  This new finding motivates a simple but novel post-selection adaptive LASSO, which we call the twin adaptive LASSO (TAlasso), to restore variable selection consistency. Accommodating 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.