On generalized Cramér-Rao inequalities, generalized Fisher informations and characterizations of generalized q-Gaussian distributionsReport as inadecuate




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1 LIGM - Laboratoire d-Informatique Gaspard-Monge

Abstract : This paper deals with Cramér-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 Cramér-Rao inequalities for the estimation of a parameter, involving general q-moments of the estimation error, ii the derivation of Cramér-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.





Author: Jean-François Bercher -

Source: https://hal.archives-ouvertes.fr/



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