Some results on a χ-divergence, an extended Fisher information and generalized Cramér-Rao inequalities

Abstract : We propose a modified χβ-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cramér-Rao inequalities, involving this Fisher information, an extension of the Fisher information matrix, and arbitrary norms and power of the estimation error. In the case of a location parameter, we obtain new characterizations of the generalized q-Gaussians, for instance as the distribution with a given moment that minimizes the generalized Fisher information. Finally we indicate how the generalized Fisher information can lead to new uncertainty relations.
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Contributor : Jean-François Bercher <>
Submitted on : Monday, May 27, 2013 - 2:56:00 PM
Last modification on : Wednesday, April 11, 2018 - 12:12:03 PM
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Jean-François Bercher. Some results on a χ-divergence, an extended Fisher information and generalized Cramér-Rao inequalities. F. Nielsen and F. Barbaresco. Geometric Science of Information, Springer, pp.487-494, 2013, First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings, 978-3-642-40019-3. ⟨10.1007/978-3-642-40020-9_53⟩. ⟨http://link.springer.com/chapter/10.1007/978-3-642-40020-9_53⟩. ⟨hal-00826445⟩

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