ON AN ADAPTIVE TRANSFORMATION-RETRANSFORMATION ESTIMATE OF MULTIVARIATE LOCATION

An affine equivariant estimate of multivariate location based on an ad aptive transformation and retransformation approach is studied. The wo rk is primarily motivated by earlier work on different versions of the multivariate median and their properties. We explore an issue related to efficiency and equivariance that was originally raised by Bickel a nd subsequently investigated by Brown and Hettmansperger. Our estimate has better asymptotic performance than the vector of co-ordinatewise medians when the variables are substantially correlated. The finite sa mple performance of the estimate is investigated by using Monte Carlo simulations. Some examples are presented to demonstrate the effect of the adaptive transformation-retransformation strategy in the construct ion of multivariate location estimates for real data.