RÉNYI DIVERGENCE AND THE CENTRAL LIMIT THEOREM

We explore properties of the χ² 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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Bibliographic Details
Published in:The Annals of probability 2019-01, Vol.47 (1), p.270-323
Main Authors: Bobkov, S. G., Chistyakov, G. P., Götze, F.
Format: Article
Language:English
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Description
Summary:We explore properties of the χ² 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).
ISSN:0091-1798
2168-894X
DOI:10.1214/18-AOP1261