Fisher-Rao distance on the covariance cone
Statistics Theory
2020-11-02 v1 Differential Geometry
Statistics Theory
Abstract
The Fisher-Rao geodesic distance on the statistical manifold consisting of zero-mean p-dimensional multivariate Gaussians appears without proof in several places (such as Steven Smith's "Covariance, Subspace, and Intrinsic Cramer-Rao Bounds"). In this paper, we give a proof using basic Riemannian geometry.
Keywords
Cite
@article{arxiv.2010.15861,
title = {Fisher-Rao distance on the covariance cone},
author = {Joseph Wells and Mary Cook and Karleigh Pine and Benjamin D. Robinson},
journal= {arXiv preprint arXiv:2010.15861},
year = {2020}
}