Tail dependence: OLS estimators under heavy-tails
This thesis shows that if the errors in a multiple regression model are heavy-tailed, the OLS estimators are tail dependent. The presence of heavy-tailed regression errors does not impair the Ftest for joint tests on the regression coefficients. However, we show that it does change the dependence structure between the two main components of the F-statistic: the fitted sum of squares (FSS) and the residual sum of squares (RSS) become strongly tail dependent — which is in contrast to the fact that they are independent when the regression errors follow a normal distribution. The tail dependence between the OLS estimators, and that between the components of the F-statistic, follow from the fact that stochastic linear (and quadratic) combinations of heavy-tailed random variables are tail dependent.