{"ID":2889739,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.21022","arxiv_id":"2507.21022","title":"A Generalized Cramér-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 Cramér-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 Cramér-Rao bound using Amari-Nagaoka's approach. There are potential applications for this bound in robust estimation.","short_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...","url_abs":"https://arxiv.org/abs/2507.21022","url_pdf":"https://arxiv.org/pdf/2507.21022v1","authors":"[\"Satyajit Dhadumia\",\"M. Ashok Kumar\"]","published":"2025-07-28T17:43:06Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"cs.IT\",\"stat.OT\"]","methods":"[]","has_code":false}