Computing depth contours of bivariate point clouds

In this paper we construct an exact algorithm for computing depth contours of a bivariate data set. For this we use the half-space depth introduced by Tukey. The depth contours form a nested collection of convex sets. The deeper the contour, the more robust it is with respect to outliers in the point cloud. The proposed algorithm has been implemented in a program called ISODEPTH, which needs little computation time and is illustrated on some real data examples. Finally, it is shown how depth contours can be used to construct robustified versions of classification techniques based on convex hulls.