The authors, Hui Zou and Runze Li, respond to the discussants' comments on their work, focusing on theoretical and computational aspects of variable selection in nonconcave penalized likelihood models. They highlight the computational challenges of optimizing $L_0$-penalized likelihood functions and the advantages of using continuous penalties like the $L_1$ penalty, which leads to methods such as LASSO. The SCAD penalty, another nonconcave penalty, is noted for its asymptotic unbiasedness and oracle properties, though it is computationally more complex than LASSO. The authors discuss the evolution of LASSO, emphasizing the role of the LARS algorithm in making it computationally efficient and popular. They introduce the LLA algorithm, which unifies LASSO and SCAD by treating them as iteratively re-weighted ridge regression, and argue that it provides a better framework for sparse estimation compared to the LQA algorithm. The LLA algorithm naturally produces sparse solutions and can be solved using the LARS algorithm. The discussion also covers the adaptive LASSO, which addresses theoretical limitations of LASSO by using adaptively weighted $L_1$ penalties. The authors explore the connection between the one-step sparse estimation idea and the adaptive LASSO, suggesting that the one-step estimator can achieve asymptotic efficiency with a good initial estimator. They also address the potential of multiple-step estimators, such as MSA-LASSO, and the importance of reducing false positives in high-dimensional data analysis. Finally, the authors discuss the Bayesian approach to variable selection, noting its probabilistic insights and flexibility in semiparametric regression models. They conclude by acknowledging the stimulating comments and the platform provided by the discussants.The authors, Hui Zou and Runze Li, respond to the discussants' comments on their work, focusing on theoretical and computational aspects of variable selection in nonconcave penalized likelihood models. They highlight the computational challenges of optimizing $L_0$-penalized likelihood functions and the advantages of using continuous penalties like the $L_1$ penalty, which leads to methods such as LASSO. The SCAD penalty, another nonconcave penalty, is noted for its asymptotic unbiasedness and oracle properties, though it is computationally more complex than LASSO. The authors discuss the evolution of LASSO, emphasizing the role of the LARS algorithm in making it computationally efficient and popular. They introduce the LLA algorithm, which unifies LASSO and SCAD by treating them as iteratively re-weighted ridge regression, and argue that it provides a better framework for sparse estimation compared to the LQA algorithm. The LLA algorithm naturally produces sparse solutions and can be solved using the LARS algorithm. The discussion also covers the adaptive LASSO, which addresses theoretical limitations of LASSO by using adaptively weighted $L_1$ penalties. The authors explore the connection between the one-step sparse estimation idea and the adaptive LASSO, suggesting that the one-step estimator can achieve asymptotic efficiency with a good initial estimator. They also address the potential of multiple-step estimators, such as MSA-LASSO, and the importance of reducing false positives in high-dimensional data analysis. Finally, the authors discuss the Bayesian approach to variable selection, noting its probabilistic insights and flexibility in semiparametric regression models. They conclude by acknowledging the stimulating comments and the platform provided by the discussants.