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High-dimensional robust inference for censored linear models

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Abstract

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).

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 12071483). The authors thank two referees for their constructive comments leading to significant improvements in the article.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Jiayu Huang

  2. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Yuanshan Wu

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  1. Jiayu Huang
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  2. Yuanshan Wu
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Correspondence to Yuanshan Wu.

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Huang, J., Wu, Y. High-dimensional robust inference for censored linear models. Sci. China Math. 67, 891–918 (2024). https://doi.org/10.1007/s11425-022-2070-2

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