Regularized distributions and entropic stability of Cramer’s characterization of the normal law

For regularized distributions we establish stability of the characterization of the normal law in Cramer’s theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are refined for random variables with finite second moment.

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Bibliographic Details
Published in:Stochastic processes and their applications 2016-12, Vol.126 (12), p.3865-3887
Main Authors: Bobkov, S.G., Chistyakov, G.P., Götze, F.
Format: Article
Language:English
Subjects:
Cramer’s theorem
Normal characterization
Stability problems
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Summary:For regularized distributions we establish stability of the characterization of the normal law in Cramer’s theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are refined for random variables with finite second moment.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2016.04.010