A Generalized Cramér-Rao Bound Using Information Geometry
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912505923633152 |
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| author | Dhadumia, Satyajit Kumar, M. Ashok |
| author_facet | Dhadumia, Satyajit Kumar, M. Ashok |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21022 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generalized Cramér-Rao Bound Using Information Geometry Dhadumia, Satyajit Kumar, M. Ashok Statistics Theory Information Theory Other Statistics 62F10, 62F35 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. |
| title | A Generalized Cramér-Rao Bound Using Information Geometry |
| topic | Statistics Theory Information Theory Other Statistics 62F10, 62F35 |
| url | https://arxiv.org/abs/2507.21022 |