Some properties of Fréchet medians in Riemannian manifolds

The consistency of Fr\échet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fr\échet medians are estimated. It is also shown that, in compact Riemannian manifolds, the Fr\échet sample medians of generic data points are always unique.