This paper shows that if the errors in a multiple regression model are heavy-tailed, the ordinary least squares (OLS) estimators for the regression coefficients are tail-dependent. The tail dependence arises, because the OLS estimators are stochastic linear combinations of heavy-tailed random variables. Moreover, tail dependence also exists between the fitted sum of squares (FSS) and the residual sum of squares (RSS), because they are stochastic quadratic combinations of heavy-tailed random variables.

中文翻译：

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OLS 的尾部依赖性

本文表明，如果多元回归模型中的误差是重尾的，则回归系数的普通最小二乘 (OLS) 估计量是尾依赖的。出现尾依赖，因为 OLS 估计量是重尾随机变量的随机线性组合。此外，拟合平方和（FSS）和残差平方和（RSS）之间也存在尾依赖，因为它们是重尾随机变量的随机二次组合。