 |
HAL UPEC - UPEM Portal |  |
 |
Book sections
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 <>
Submitted on : Monday, May 27, 2013 - 2:56:00 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:06 PM
Long-term archiving on: : Wednesday, August 28, 2013 - 4:35:09 AM
Contributor : Jean-François Bercher <>
Submitted on : Monday, May 27, 2013 - 2:56:00 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:06 PM
Long-term archiving on: : Wednesday, August 28, 2013 - 4:35:09 AM