High-dimensional robust inference for censored linear models  

作　　者：Jiayu Huang Yuanshan Wu 

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China [2]School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China

出　　处：《Science China Mathematics》2024年第4期891-918,共28页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12071483)。

摘　　要：Due to the direct statistical interpretation,censored linear regression offers a valuable complement to the Cox proportional hazards regression in survival analysis.We propose a rank-based high-dimensional inference for censored linear regression without imposing any moment condition on the model error.We develop a theory of the high-dimensional U-statistic,circumvent challenges stemming from the non-smoothness of the loss function,and establish the convergence rate of the regularized estimator and the asymptotic normality of the resulting de-biased estimator as well as the consistency of the asymptotic variance estimation.As censoring can be viewed as a way of trimming,it strengthens the robustness of the rank-based high-dimensional inference,particularly for the heavy-tailed model error or the outlier in the presence of the response.We evaluate the finite-sample performance of the proposed method via extensive simulation studies and demonstrate its utility by applying it to a subcohort study from The Cancer Genome Atlas(TCGA).

关 键 词：censoring mechanism heavy-tailed distribution non-smooth loss function OUTLIER rank regression 

分 类 号：O212.1[理学—概率论与数理统计]