Some properties of Fréchet medians in Riemannian manifolds

Le Yang (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]

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.

Mots clés: Fréchet median; probability measure; Riemannian manifold

Domaines: Géométrie différentielle [math.DG]; Statistiques [math.ST]; Théorie [stat.TH]; Probabilités [math.PR]

Le Yang. Some properties of Fréchet medians in Riemannian manifolds. 2011. ⟨hal-00633203v2⟩