Some properties of Fréchet medians in Riemannian manifolds
Le Yang · arXiv (Cornell University) · 2011
The consistency of Fréchet 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 Fréchet medians are estimated. It is also shown that, in compact Riemannian manifolds, the Fréchet sample medians of generic data points are always unique.