TAIL DEPENDENCE OF OLS
证明在多元回归模型误差为重尾分布时,普通最小二乘估计量之间存在尾部相依性,且拟合平方和与残差平方和也存在尾部相依性。
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.