Simultaneous variable selection and estimation for survival data via the Gaussian seamless- L 0 $$ {L}_0 $$ penalty.

We propose a new simultaneous variable selection and estimation procedure with the Gaussian seamless- L 0 $$ {L}_0 $$ (GSELO) penalty for Cox proportional hazard model and additive hazards model. The GSELO procedure shows good potential to improve the existing variable selection methods by taking strength from both best subset selection (BSS) and regularization. In addition, we develop an iterative algorithm to implement the proposed procedure in a computationally efficient way. Theoretically, we establish the convergence properties of the algorithm and asymptotic theoretical properties of the proposed procedure. Since parameter tuning is crucial to the performance of the GSELO procedure, we also propose an extended Bayesian information criteria (EBIC) parameter selector for the GSELO procedure. Simulated and real data studies have demonstrated the prediction performance and effectiveness of the proposed method over several state-of-the-art methods.