Oja Median: Center-Locating Property

Abstract

The property of consistency with the point of symmetry is a natural requirement for an arbitrary estimate of the center (for the centrally symmetric distribution this follows from the affine equivariance of the estimate). Different notions of multidimensional symmetry and some of their properties are given in this paper. We establish that in the general case, the multidimensional simplicial Oja median identifies the point of symmetry, if it exists. By this criterion we compare the Oja median with the other best-known multidimensional medians.