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

  • Jean-François Bercher
Conference paper

DOI: 10.1007/978-3-642-40020-9_53

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8085)
Cite this paper as:
Bercher JF. (2013) Some Results on a χ-divergence, an Extended Fisher Information and Generalized Cramér-Rao Inequalities. In: Nielsen F., Barbaresco F. (eds) Geometric Science of Information. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg

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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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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