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

An affine equivariant version of multivariate median is introduced. The 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 construction of the median has some fundamental connection with the data driven co-ordinate system considered by Chaudhuri and Sengupta (1993, Journal of the American Statistical Association ). large sample statistical properties of the median are discussed and finite sample performance is investigated using Monte Carlo simulation.