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arXiv · 1206.0567

On generalized Cram\'er-Rao inequalities, generalized Fisher informations and characterizations of generalized q-Gaussian distributions

J. -F. Bercher
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Abstract

This paper deals with Cram\'er-Rao inequalities in the context of nonextensive statistics and in estimation theory. It gives characterizations of generalized q-Gaussian distributions, and introduces generalized versions of Fisher information. The contributions of this paper are (i) the derivation of new extended Cram\'er-Rao inequalities for the estimation of a parameter, involving general q-moments of the estimation error, (ii) the derivation of Cram\'er-Rao inequalities saturated by generalized q-Gaussian distributions, (iii) the definition of generalized Fisher informations, (iv) the identification and interpretation of some prior results, and finally, (v) the suggestion of new estimation methods.

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J. -F. Bercher. 2012-06-04. On generalized Cram\'er-Rao inequalities, generalized Fisher informations and characterizations of generalized q-Gaussian distributions. https://doi.org/10.1088/1751-8113/45/25/255303

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