ON A TRANSFORMATION AND RE-TRANSFORMATION TECHNIQUE FOR CONSTRUCTING AN AFFINE EQUIVARIANT MULTIVARIATE MEDIAN

An affine equivariant version of multivariate median is introduced. Th e proposed median is easy to compute and has some appealing geometric features that are related to the configuration of a multivariate data cloud. The transformation and re-transformation approach used in the c onstruction of the median has some fundamental connection with the dat a driven co-ordinate system considered by Chaudhuri and Sengupta (1993 , Journal of the American Statistical Association). Large sample stati stical properties of the median are discussed and finite sample perfor mance is investigated using Monte Carlo simulations.