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This œuvre, Kernel Density Estimation on Symmetric Spaces, by Dena Asta is licensed under a Creative Commons Attribution-ShareAlike 4.0 International license.

Kernel Density Estimation on Symmetric Spaces


Kernel Density Estimation on Symmetric Spaces
Publication details: 
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.
Source et DOI
Kernel Density Estimation on Symmetric Spaces
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