ORTHOGONALIZATION OF MULTIVARIATE LOCATION ESTIMATORS - THE ORTHOMEDIAN

The coordinatewise median of a multivariate data set is a highly robus t location estimator. but it depends on the choice of coordinates. A p opular alternative which avoids this drawback is the spatial median, d efined as the value that minimizes the sum of distances to the individ ual data points. In this paper are introduce and discuss another ortho gonal equivariant version of the multivariate median, obtained by aver aging the coordinatewise median over all orthogonal transformations. W e investigate the asymptotic behavior of this estimator and compare it to the spatial median.