Variable selection and structure identification for varying coefficient Cox models

We consider varying coefficient Cox models with high-dimensional covariates. We apply the group Lasso to these models and propose a variable selection procedure. Our procedure can cope with simultaneous variable selection and structure identification for high-dimensional varying coefficient models to find true semi-varying coefficient models from them. We also derive an oracle inequality and closely examine restrictive eigenvalue conditions. We focus on Cox models with time-varying coefficients. The theoretical results on variable selection can be extended easily to some other important models which we only mention briefly since they can be treated in the same way. The models considered here are the most popular among structured nonparametric regression models. The results of numerical studies are also reported.