标题： 非渐近 oracle 不等式对于使用 Lasso 的高维 Cox 回归 显示英文标题

标题： Non-asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso

摘要： 我们研究了通过套索正则化的高维Cox回归的有限样本性质。现有文献主要集中在线性模型或具有Lipschitz损失函数的广义线性模型上，其中经验风险函数是独立同分布（iid）损失的总和。然而，删失生存数据的部分似然函数的负对数和项既不是iid也不是Lipschitz。我们首先通过一组iid的非Lipschitz项来近似负部分似然函数的对数，然后利用逐点论证推导出套索惩罚Cox回归的非渐近oracle不等式，以解决缺乏iid和Lipschitz性质所带来的困难。 显示英文摘要

摘要： We consider the 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 difficulty caused by the lack of iid and Lipschitz property.