Employing the Lorentzian seamless- \(L_0\) penalty, we introduce a penalized variable selection procedure that adeptly combines variable selection and parameter estimation within the framework of the proportional sub-distribution hazards model. This novel strategy exhibits promising potential to surpass existing variable selection methodologies by harnessing the strengths of both the best subset selection and regularization techniques. To ensure computational efficiency, an iterative algorithm tailored to the proposed methodology is also implemented. On the theoretical front, we rigorously prove the convergence characteristics of our algorithm and establish the asymptotic properties of the LSELO procedure. Recognizing the paramount importance of parameter tuning for optimal LSELO performance, we present an extended Bayesian information criteria selector specifically designed for this purpose. Extensive evaluations using both simulated and real-world datasets have convincingly demonstrated the superior performance of our method compared to several cutting-edge alternatives in the field.
