Robust post-selection inference of high-dimensional mean regression with heavy-tailed asymmetric or heteroskedastic errors
针对高维线性模型中误差重尾且非对称的情况，基于Huber损失提出一种稳健的后选择推断方法，并扩展至异方差情形，用于回归系数的统计检验。
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.