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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.
Cited literature [19 references]
https://hal-upec-upem.archives-ouvertes.fr/hal-00826445
Contributor : Jean-François Bercher Connect in order to contact the contributor
Submitted on : Monday, May 27, 2013 - 2:56:00 PM
Last modification on : Saturday, January 15, 2022 - 3:58:16 AM
Long-term archiving on: : Wednesday, August 28, 2013 - 4:35:09 AM
Contributor : Jean-François Bercher Connect in order to contact the contributor
Submitted on : Monday, May 27, 2013 - 2:56:00 PM
Last modification on : Saturday, January 15, 2022 - 3:58:16 AM
Long-term archiving on: : Wednesday, August 28, 2013 - 4:35:09 AM