On generalized Cramer-Rao inequalities, generalized Fisher information and characterizations of generalized q-Gaussian distributions
On generalized Cramer-Rao inequalities, generalized Fisher information and characterizations of generalized q-Gaussian distributions
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DOI：
10.1088/1751-8113/45/25/255303
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发表时间：
2012-06-29
影响因子：
2.1
通讯作者：
Bercher, J-F
中科院分区：
文献类型：
--
作者：
Bercher, J-F
本文在非广延统计和估计理论的背景下讨论克莱默-饶不等式。它给出了广义 q-高斯分布的特征并引入了 Fisher 信息的广义版本。本文的贡献是（i）推导用于参数估计的新扩展 Cramer-Rao 不等式，涉及估计误差的一般 q 矩，（ii）推导广义 q-高斯分布饱和的 Cramer-Rao 不等式，（iii）广义 Fisher 信息的定义，（iv）一些先前结果的识别和解释，最后（v）新估计方法的建议。
This paper deals with Cramer-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 Cramer-Rao inequalities for the estimation of a parameter, involving general q-moments of the estimation error, (ii) the derivation of Cramer-Rao inequalities saturated by generalized q-Gaussian distributions, (iii) the definition of generalized Fisher information, (iv) the identification and interpretation of some prior results and finally (v) the suggestion of new estimation methods.