The authors of this rejoinder thank the discussants for their comments and address several issues raised regarding variable selection in nonconcave penalized likelihood models. They explain that traditional variable selection criteria like AIC and BIC are equivalent to the L0 penalty, which is computationally challenging. However, under sparsity assumptions, the L0 penalty can be approximated by solving a convex optimization problem with the L1 penalty. This motivates the use of continuous penalties like L1 instead of the discontinuous L0 penalty. LASSO and SCAD are two main methods for variable selection, with SCAD having better theoretical properties than LASSO. The LQA algorithm unifies LASSO and SCAD as iteratively reweighted ridge regression, but it is not satisfactory due to the need for manual thresholding. The LLA algorithm provides a better unification, as it naturally produces sparse solutions. The one-step sparse estimator, which is efficient and has oracle properties, is shown to perform well. The adaptive LASSO, which uses an adaptive L1 penalty, is also discussed. The authors agree that the one-step estimator can be viewed as a type of early stopping in boosting. They also mention the MSA-LASSO algorithm, which is a multiple-step estimator. The paper discusses the connection between penalized likelihood and Bayesian approaches, noting that penalized likelihood can be seen as a Bayesian method without the need for a prior. The authors also discuss the computational efficiency of the one-step estimator and its potential in high-dimensional data analysis. The paper concludes with a discussion on the importance of sparsity in high-dimensional data and the potential of the one-step estimator in practical applications.The authors of this rejoinder thank the discussants for their comments and address several issues raised regarding variable selection in nonconcave penalized likelihood models. They explain that traditional variable selection criteria like AIC and BIC are equivalent to the L0 penalty, which is computationally challenging. However, under sparsity assumptions, the L0 penalty can be approximated by solving a convex optimization problem with the L1 penalty. This motivates the use of continuous penalties like L1 instead of the discontinuous L0 penalty. LASSO and SCAD are two main methods for variable selection, with SCAD having better theoretical properties than LASSO. The LQA algorithm unifies LASSO and SCAD as iteratively reweighted ridge regression, but it is not satisfactory due to the need for manual thresholding. The LLA algorithm provides a better unification, as it naturally produces sparse solutions. The one-step sparse estimator, which is efficient and has oracle properties, is shown to perform well. The adaptive LASSO, which uses an adaptive L1 penalty, is also discussed. The authors agree that the one-step estimator can be viewed as a type of early stopping in boosting. They also mention the MSA-LASSO algorithm, which is a multiple-step estimator. The paper discusses the connection between penalized likelihood and Bayesian approaches, noting that penalized likelihood can be seen as a Bayesian method without the need for a prior. The authors also discuss the computational efficiency of the one-step estimator and its potential in high-dimensional data analysis. The paper concludes with a discussion on the importance of sparsity in high-dimensional data and the potential of the one-step estimator in practical applications.