Kernel Density Estimation on Symmetric Spaces of Non-Compact Type

Dena Marie Asta

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arXiv · 1411.4040

Kernel Density Estimation on Symmetric Spaces of Non-Compact Type

Dena Marie Asta

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Abstract

We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric spaces of non-compact type include hyperboloids of constant negative curvature and spaces of symmetric positive definite matrices. This paper obtains a simplified formula in the special case when the symmetric space is the space of normal distributions, a 2-dimensional hyperboloid.

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Dena Marie Asta. 2014-11-14. Kernel Density Estimation on Symmetric Spaces of Non-Compact Type. https://arxiv.org/abs/1411.4040

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