Open Access
January 2019 Rényi divergence and the central limit theorem
S. G. Bobkov, G. P. Chistyakov, F. Götze
Ann. Probab. 47(1): 270-323 (January 2019). DOI: 10.1214/18-AOP1261


We explore properties of the $\chi^{2}$ and Rényi distances to the normal law and in particular propose necessary and sufficient conditions under which these distances tend to zero in the central limit theorem (with exact rates with respect to the increasing number of summands).


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S. G. Bobkov. G. P. Chistyakov. F. Götze. "Rényi divergence and the central limit theorem." Ann. Probab. 47 (1) 270 - 323, January 2019.


Received: 1 October 2016; Revised: 1 January 2018; Published: January 2019
First available in Project Euclid: 13 December 2018

zbMATH: 07036338
MathSciNet: MR3909970
Digital Object Identifier: 10.1214/18-AOP1261

Primary: 60E , 60F15

Keywords: $\chi^{2}$-divergence , central limit theorem , Rényi and Tsallis entropies

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.47 • No. 1 • January 2019
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