Nonparametric Model Selection in Hazard Regression

We propose a novel model selection method for a nonparametric extension of the Cox proportional hazard model, in the framework of smoothing splines ANOVA models. The method automates the model building and model selection process simultaneously by imposing a penalty on the norms instead of squared norms. It is a natural extension of the LASSO to the situation where component selection is of interest. We further propose an efficient algorithm based on a reformulation of the penalized likelihood. Adaptive choice of the smoothing parameter is discussed. Both simulations and real examples suggest that our proposal is very powerful for model selection and component estimation in survival analysis. MSC : 62N02, 62G08.