Generalized and robustified empirical depths for multivariate data

In this paper, we point out a common feature of zonoid and empirical depths that gives rise to a novel class of data depths, and provide a possible robustification of their deepest points. This general approach may be useful as it allows the robustification of the zonoid depth and other depths that are centered at the usual mean. Illustrations are also provided to demonstrate the depth contours induced from these depths based on a real data set. (C) 2018 Elsevier B.V. All rights reserved.