This paper considers inference in a linear regression model with random right censoring and outliers. The number of outliers can grow with the sample size while their proportion goes to zero. The model is semiparametric and we make only very mild assumptions on the distribution of the error term, contrary to most other existing approaches in the literature. We propose to penalize the estimator proposed by Stute for censored linear regression by the l1-norm. We derive rates of convergence and establish asymptotic normality of the estimator of the regression coefficients. Our estimator has the same asymptotic variance as Stute's estimator in the censored linear model without outliers. Hence, there is no loss of efficiency as a result of robustness. Tests and confidence sets can therefore rely on the theory developed by Stute. The outlined procedure is also computationally advantageous, since it amounts to solving a convex optimization program. We also propose a second estimator which uses the proposed penalized Stute estimator as a first step to detect outliers. It has similar theoretical properties but better performance in finite samples as assessed by simulations.

翻译：本文用随机右检查和外部线条来考虑线性回归模型中的推论。 外部线人的数量可以随着抽样规模的增加而增长, 而其比例则变为零。 模型是半参数, 我们仅对错误术语的分布作出非常温和的假设, 与文献中的大多数其他现有方法相反。 我们提议惩罚Stute为l1- 诺尔姆受审查的线性回归提议的估计值。 我们得出趋同率, 并确立回归系数估计值的无症状常态。 我们的估计值与Stute在经审查的线条模型中的估计值有相同的非症状差异, 没有外线条值。 因此, 没有因稳健性而丧失效率。 因此, 测试和信任组可以依赖 Stute 开发的理论。 概述程序也具有计算优势, 因为它相当于解决一个 convex 优化程序 。 我们还提议了第二个估算器, 它将拟议的惩罚 Stute 估测算器作为检测外线条的第一步。 它具有相似的理论属性, 但通过模拟得到更好的表现。