ON MULTIVARIATE RANK REGRESSION

An extension of rank regression technique to multivariate linear models is proposed and studied. Unlike the coordinatewise rank regression techniques considered by some earlier authors, our approach is affine equivariant, and it is based on a transformation and retransformation procedure originally developed by Chakraborty and Chaudhuri (1996, 1998) for constructing an affine equivariant version of multivariate median. Affine equivariance is expected to lead to superior statistical performance of our procedure compared to other non-equivariant procedures especially in the presence of substantial correlations among different response variables in multi-response problems. Some of the statistical properties of the proposed multivariate rank regression estimates are discussed, and a few results based on numerical investigation of the performance of these estimates are presented.