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线性回归模型是稳健建模的常用方法之一，在文献中被广泛采用。然而，大多数应用在缺乏严谨理论考量的情况下直接使用该模型。本研究基于正则变化理论，提出了实用且简洁的条件，以确保学生-t线性回归模型在y方向异常值存在时具备稳健性。