%0 Journal Article
%T Existence and Consistency of Wasserstein Barycenters
%+ Institut de Mathématiques de Marseille (I2M)
%+ Institut de Mathématiques de Toulouse UMR5219 (IMT)
%A Le Gouic, Thibaut
%A Loubes, Jean-Michel
%< avec comité de lecture
%@ 0178-8051
%J Probability Theory and Related Fields
%I Springer Verlag
%V 168
%N 3-4
%P 901-917
%8 2017-08
%D 2017
%Z 1506.04153
%R 10.1007/s00440-016-0727-z
%Z Mathematics [math]/Statistics [math.ST]Journal articles
%X In this paper, based on the Fréchet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random distributions defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the distributions or of a growing set of distributions.
%G English
%2 https://hal.science/hal-01163262v2/document
%2 https://hal.science/hal-01163262v2/file/DepthWasser.pdf
%L hal-01163262
%U https://hal.science/hal-01163262
%~ UNIV-TLSE2
%~ UNIV-TLSE3
%~ CNRS
%~ UNIV-AMU
%~ INSA-TOULOUSE
%~ EC-MARSEILLE
%~ IMT
%~ I2M
%~ I2M-2014-
%~ UT1-CAPITOLE
%~ INSA-GROUPE
%~ TEST-HALCNRS
%~ UNIV-UT3
%~ UT3-INP
%~ UT3-TOULOUSEINP
%~ TEST3-HALCNRS