Kernel Density Estimation on Symmetric Spaces - Dena Asta
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last edited by Geo-Sci-InfoAuthor: Dena Asta
DOI URL: http://dx.doi.org/10.1007/978-3-319-25040-3_83
Video: Not available
Slides: https://drive.google.com/open?id=0B0QKxsVtOaTiX0lnY3YzZDV1Y0E
Presentation: https://www.see.asso.fr/node/14314
Creative Commons Attribution-ShareAlike 4.0 InternationalAbstract:
We introduce a novel kernel density estimator for a large class of symmetric spaces and prove a minimax rate of convergence as fast as the minimax rate on Euclidean space. We prove a minimax rate of convergence proven without any compactness assumptions on the space or Hölder-class assumptions on the densities. A main tool used in proving the convergence rate is the Helgason-Fourier transform, a generalization of the Fourier transform for semisimple Lie groups modulo maximal compact subgroups. This paper obtains a simplified formula in the special case when the symmetric space is the 2-dimensional hyperboloid.
