High-dimensional robust inference for censored linear models

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).