In this paper, we first describe the generalized notion of Cramer-Rao lower bound obtained by Naudts (2004) using two families of probability density functions, the original model and an escort model. We reinterpret the results in Naudts (2004) from a statistical point of view and obtain some interesting examples in which this bound is attained. Further we obtain information inequalities which generalize the classical Bhattacharyya bounds in both regular and non-regular cases.

中文翻译：

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统计推断的一些信息不等式

在本文中，我们首先描述了 Naudts (2004) 使用两个概率密度函数族，原始模型和护送模型获得的 Cramer-Rao 下界的广义概念。我们从统计的角度重新解释了 Naudts (2004) 中的结果，并获得了一些有趣的例子，其中达到了这个界限。此外，我们获得了信息不等式，这些不等式在常规和非常规情况下推广了经典的 Bhattacharyya 界限。