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，大多数应用缺乏严谨的理论考量。本研究通过正则变化理论，提供了实用且简洁的条件，以确保学生t线性回归模型对y方向上的异常值具有稳健性。