Distribution of an arbitrary linear transformation of internally Studentized residuals of multivariate regression with elliptical errors

This paper derives the matrix-variate distribution of an arbitrary non-singular linear transformation of Studentized multivariate observations. The joint distributions of the major commonly utilized Studentized versions of (multivariate) regression residuals are obtained as special cases of the matrix-variate distribution introduced in the paper. As applications, the paper discusses testing for outliers, omitted variables, and general linear hypothesis in terms of Studentized linear combinations of residuals.