Corpus ID: 126085629

On the rate of convergence of empirical barycentres in metric spaces: curvature, convexity and extendible geodesics

@article{AhidarCoutrix2019OnTR,
  title={On the rate of convergence of empirical barycentres in metric spaces: curvature, convexity and extendible geodesics},
  author={Adil Ahidar-Coutrix and Thibaut Le Gouic and Q. Paris},
  journal={arXiv: Statistics Theory},
  year={2019}
}
  • Adil Ahidar-Coutrix, Thibaut Le Gouic, Q. Paris
  • Published 2019
  • Mathematics
  • arXiv: Statistics Theory
  • 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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