Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendible geodesics.

@inproceedings{AhidarCoutrix2018ConvergenceRF,
  title={Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendible geodesics.},
  author={Adil Ahidar-Coutrix and Thibaut Le Gouic and Quentin Paris},
  year={2018}
}
This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumption is termed a variance inequality and provides a strong connection between usual assumptions in the field of empirical processes and central concepts of metric geometry. We study the validity of variance inequalities in spaces of non-positive and non-negative Aleksandrov curvature. In this last… CONTINUE READING
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