Barycenter in Wasserstein space existence and consistency

Thibaut Le Gouic (1) , Jean-Michel Loubes (2)

1 I2M - Institut de Mathématiques de Marseille
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We study barycenters in the Wasserstein space Pp(E) of a locally compact geodesic space (E, d). In this framework, we define the barycenter of a measure P on Pp(E) as its Fréchet mean. The paper establishes its existence and states consistency with respect to P. We thus extends previous results on R^d , with conditions on P or on the sequence converging to P for consistency.

Mots clés: barycenter; Wasserstein space; geodesic spaces

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Thibaut Le Gouic, Jean-Michel Loubes. Barycenter in Wasserstein space existence and consistency. GSI2015 2nd conference on Geometric Science of Information, Oct 2015, Palaiseau, France. pp.104-108, ⟨10.1007/978-3-319-25040-3_12⟩. ⟨hal-01291307⟩