Model pursuit and variable selection in the additive accelerated failure time model

In this paper, we propose a new semiparametric method to simultaneously select important variables, identify the model structure and estimate covariate effects in the additive AFT model, for which the dimension of covariates is allowed to increase with sample size. Instead of directly approximating the non-parametric effects as in most existing studies, we take a linear effect out to weak the condition required for model identifiability. To compute the proposed estimates numerically, we use an alternating direction method of multipliers algorithm so that it can be implemented easily and achieve fast convergence rate. Our method is proved to be selection consistent and possess an asymptotic oracle property. The performance of the proposed methods is illustrated through simulations and the real data analysis.