Kernel Density Estimation on Symmetric Spaces release_nebec3pfsvh4neyjk7577mue5u

by Dena Marie Asta

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2014  

Abstract

We investigate a natural variant of kernel density estimation on a large class of symmetric spaces and prove a minimax rate of convergence as fast as the minimax rate on Euclidean space. We make neither compactness assumptions on the space nor Holder-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.
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Date   2014-11-14
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Language   en ?
arXiv  1411.4040v1
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