Rényi divergence and the central limit theorem

By S. G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze. 2016

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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.

Subfields: Finance, Statistical and Nonlinear Physics, Statistics and Probability