An optimal randomized algorithm for d-variate zonoid depth

A randomized linear expected-time algorithm for computing the zonoid depth [R. Dyckerhoff, G. Koshevoy, K. Mosler, Zonoid data depth: Theory and computation, in: A. Prat (Ed.), COMPSTAT 1996—Proceedings in Computational Statistics, Physica-Verlag, Heidelberg, 1996, pp. 235–240; K. Mosler, Multivariate Dispersion, Central Regions and Depth. The Lift Zonoid Approach, Lecture Notes in Statistics, vol. 165, Springer-Verlag, New York, 2002] of a point with respect to a fixed dimensional point set is presented.