For the outlier problem in linear regression models, the Student-$t$ linear regression model is one of the common methods for robust modeling and is widely adopted in the literature. However, most of them applies it without careful theoretical consideration. This study provides the practically useful and quite simple conditions to ensure that the Student-$t$ linear regression model is robust against an outlier in the $y$-direction using regular variation theory.

翻译：针对线性回归模型中的异常值问题，学生-t线性回归模型是进行稳健建模的常用方法之一，并在文献中得到广泛应用。然而，多数研究在应用该模型时缺乏充分的理论考量。本研究利用正则变化理论，提出了确保学生-t线性回归模型在y方向异常值场景下保持稳健性的实用且简洁条件。