Some Results on a χ-divergence, an Extended Fisher Information and Generalized Cramér-Rao Inequalities

  • Jean-François Bercher
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8085)


We propose a modified χ β -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.


Uncertainty Relation Fisher Information Fisher Information Matrix Quadratic Case Arbitrary Norm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jean-François Bercher
    • 1
  1. 1.Laboratoire d’Informatique Gaspard Monge, UMR 8049Université Paris-Est, ESIEENoisy-le-Grand CedexFrance

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