Variable selection and estimation for accelerated failure time model via seamless- $L_0$ penalty

Survival data with high dimensional covariates have been collected in medical studies and other fields. In this work, we propose a seamless $L_0$ (SELO) penalized method for the accelerated failure time (AFT) model under the framework of high dimension. Specifically, we apply the SELO to do variable selection and estimation under this model. Under appropriate conditions, we show that the SELO selects a model whose dimension is comparable to the underlying model, and prove that the proposed procedure is asymptotically normal. Simulation results demonstrate that the SELO procedure outperforms other existing procedures. The real data analysis is considered as well which shows that SELO selects the variables more correctly.