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On generalized Cramér-Rao inequalities, generalized Fisher informations and characterizations of generalized q-Gaussian distributions (1206.0567v1)
Published 4 Jun 2012 in math-ph, cond-mat.stat-mech, cs.IT, math.IT, and math.MP
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.