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Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics
This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumptionExpand
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On the rate of convergence of empirical barycentres in metric spaces: curvature, convexity and extendible geodesics
This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumptionExpand
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Surfaces quantile : propriétés, convergences et applications
The main issue of the thesis is the development of spatial generalizations on $\R^d$ of the usual real quantile. Facing the usual fact that $\R^d$ is not naturally ordered, our idea is to simplyExpand
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Convergence of Multivariate Quantile Surfaces
We define the quantile set of order α ∈ [1/2, 1) associated to a law P on R d to be the collection of its directional quantiles seen from an observer O ∈ R d. Under minimal assumptions theseExpand