title: Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso.
abstract: We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses.
authors: Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI 48109-2029.
authors: Shengchun
authors: S
authors: Kong
authors: Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI 48109-2029.
authors: Bin
authors: B
authors: Nan
keywords: Cox regression; finite sample; lasso; oracle inequality; variable selection