Kernel Density Estimation on Symmetric Spaces of Non-Compact Type
Statistics Theory
2022-06-30 v3 Statistics Theory
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.
Cite
@article{arxiv.1411.4040,
title = {Kernel Density Estimation on Symmetric Spaces of Non-Compact Type},
author = {Dena Marie Asta},
journal= {arXiv preprint arXiv:1411.4040},
year = {2022}
}