The distribution of residuals from a general elliptical linear model

Given a general linear model of full or less than full rank, we find the distributions of normalized, standardized and studentized (internally and externally studentized) residuals, assuming normal and elliptical distributions. In addition, we propose an alternative approach to the results published by Ellenberg [1973, The joint distribution of the standardized least squares residual from general linear regression. J. Amer. Statist. Assoc. 68, 941-943] and Beckman and Trusell [1974, The distribution of an arbitrary studentized residual and effects of updating in multiple regression. J. Amer. Statist. Assoc. 69, 199-201].