A Generalized Cram\'er-Rao Bound Using Information Geometry
Abstract
In information geometry, statistical models are considered as differentiable manifolds, where each probability distribution represents a unique point on the manifold. A Riemannian metric can be systematically obtained from a divergence function using Eguchi's theory (1992); the well-known Fisher-Rao metric is obtained from the Kullback-Leibler (KL) divergence. The geometric derivation of the classical Cram\'er-Rao Lower Bound (CRLB) by Amari and Nagaoka (2000) is based on this metric. In this paper, we study a Riemannian metric obtained by applying Eguchi's theory to the Basu-Harris-Hjort-Jones (BHHJ) divergence (1998) and derive a generalized Cram\'er-Rao bound using Amari-Nagaoka's approach. There are potential applications for this bound in robust estimation.
Cite
@article{arxiv.2507.21022,
title = {A Generalized Cram\'er-Rao Bound Using Information Geometry},
author = {Satyajit Dhadumia and M. Ashok Kumar},
journal= {arXiv preprint arXiv:2507.21022},
year = {2025}
}
Comments
Presented at the IEEE International Symposium on Information Theory (ISIT 2025)