Information geometry and classical Cramér–Rao-type inequalities
نویسندگان
چکیده
Abstract We examine the role of information geometry in context classical Cramer–Rao (CR) type inequalities. In particular, we focus on Eguchi's theory obtaining dualistic geometric structures from a divergence function and then applying Amari–Nagoaka's to obtain CR inequality. The deterministic inequality is derived Kullback–Leibler (KL) divergence. show that this framework could be generalized other inequalities through four examples: ?-version inequality, Bayesian ?-CR These are obtained from, respectively, I?-divergence (or relative ?-entropy), Csiszar divergence, KL I?-divergence.
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ژورنال
عنوان ژورنال: Handbook of Statistics
سال: 2021
ISSN: ['0169-7161', '1875-7448']
DOI: https://doi.org/10.1016/bs.host.2021.07.005