Confidence intervals for high-dimensional Cox model

The purpose of this work is to construct confidence intervals for high-dimensional Cox proportional hazards regression models, where the number of time-dependent covariates can be larger than the sample size. The definition of the one-step estimator is similar to those in van de Geer et al. (2014) and Zhang and Zhang (2014), but since in the Cox regression model, the Hessian matrix is based on time-dependent covariates in censored risk sets, the technical difficulties are fundamentally different. I will talk about the related theoretical and numerical results in this talk. This is joint work with Jelena Bradic (UCSD) and Richard Samworth (Cambridge).