Title: Connecting pairwise spheres by depth: DCOPS,
Abstract: We extend the classical notion of the spherical depth in \mathbb{R}^k, to the
important setup of data on a Riemannian manifold. We show that this notion of
depth satisfies a set of desirable properties. For the empirical version of
this depth function both uniform consistency and the asymptotic distribution
are studied. Consistency is also shown for functional data. The behaviour of
the depth is illustrated through several examples for Riemannian manifold data.