Abstract
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 probabilities 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 probability measures or of a growing set of probability measures.
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Le Gouic, T., Loubes, JM. Existence and consistency of Wasserstein barycenters. Probab. Theory Relat. Fields 168, 901–917 (2017). https://doi.org/10.1007/s00440-016-0727-z
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DOI: https://doi.org/10.1007/s00440-016-0727-z