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This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques.
Les éléments aléatoires de nature quelconque dans un espace distancié
M. Fréchet · 1948
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Asymptotic Methods in Statistical Decision Theory
L. M. Le Cam · 1986
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Theory of Statistical Inference and Information
I. Vajda · 1989
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Sur le barycentre d’une probabilité dans une variété
M. Émery and G. Mokobodzki · 1991
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R. Bhattacharya and V. Patrangenaru · 2003
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C. Villani · 2003
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L. Ambrosio and P. Tilli · 2004
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Local Rademacher complexities
P. Bartlett, O. Bousquet, and S. Mendelson · 2005
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Large sample theory of intrinsic and extrinsic sample means on manifold - ii
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B. Pelletier · 2005
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