We propose a robust post-selection inference method based on the Huber loss for the regression coefficients, when the error distribution is heavy-tailed and asymmetric in a high-dimensional linear model with an intercept term. The asymptotic properties of the resulting estimators are established under mild conditions. We also extend the proposed method to accommodate heteroscedasticity assuming the error terms are symmetric and other suitable conditions. Statistical tests for low-dimensional parameters or individual coefficient in the high-dimensional linear model are also studied. Simulation studies demonstrate desirable properties of the proposed method. An application to a genomic dataset about riboflavin production rate is provided.

当误差分布在具有截距项的高维线性模型中是重尾和不对称时，我们提出了一种基于回归系数的 Huber 损失的稳健的后选择推理方法。所得估计量的渐近性质是在温和条件下建立的。我们还扩展了所提出的方法以适应异方差性，假设误差项是对称的和其他合适的条件。还研究了高维线性模型中低维参数或单个系数的统计检验。模拟研究证明了所提出方法的理想特性。提供了关于核黄素产生率的基因组数据集的应用。