Median hyperplanes in normed spaces

In this paper we deal with the location of hyperplanes in n{ dimensional normed spaces. If d is a distance measure, our objective is to nd a hyperplane H which minimizes points and d(x m ; H) = min z2H d(x m ; z) is the distance from x m to the hyperplane H. In robust statistics and operations research such an optimal hyperplane is called a median hyperplane. We show that for all distance measures d derived from norms, one of the hyper-planes minimizing f(H) is the aane hull of n of the demand points and, moreover, that each median hyperplane is (in a certain sense) a halving one with respect to the given point set.