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. (C) 2012 Elsevier Inc. All rights reserved.