Date of Original Version
18th Fall Workshop on Computational and Combinatorial Geometry, Rensselaer Polytechnic Institute, October 2008.
Abstract or Description
We generalize the Tukey depth to use cones instead of halfspaces. We prove a generalization of the center point theorem that for S ⊂ R2, there is a point s ∈S, with depth at least n/d+1 for cones of half-angle 45◦. This gives a notion of data depth for which an approximate median can always be found among the original set.