We introduce a new notion of depth of low computational complexity for high dimensional data. For small dimensions, it behaves similarly to simplicial and half-space depths. We show that this new depth notion shares the set of desirable properties that were introduced in Serfling (1980). For the empirical version of this depth function both uniform consistency and the asymptotic distribution are studied. Our new notion is extended to the important setup of data in Riemannian manifolds. The behaviour of the depth is illustrated through several examples. 查看全文>>