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).