Rényi divergence and the central limit theorem
Rényi divergence and the central limit theorem
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Rényi 散度和中心极限定理
作者：
S. G. Bobkov;G. Chistyakov;F. Götze
我们探索 $chi^2$ 和更一般的 R'enyi (Tsallis) 距离与正常定律的属性。特别是，我们使用这些距离为中心极限定理中的正常定律收敛提供了充分必要条件。此外，我们针对不断增加的被加数得出了这些距离上的精确收敛率。
We explore properties of the $chi^2$ and more general R'enyi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using these distances. Moreover, we derive exact rates of convergence in these distances with respect to an increasing number of summands.