Algorithms for bivariate zonoid depth

Zonoid depth is a definition of data depth proposed by Dyckerhoff et al. [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, August 1996, pp. 235–240]. Efficient algorithms for solving several computational problems related to zonoid depth in 2-dimensional (bivariate) data sets are studied. These include algorithms for computing a zonoid depth map, computing a zonoid depth contour, and computing the zonoid depth of a point.