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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Reversing the Berry-Esseen inequality


Authors: Peter Hall and A. D. Barbour
Journal: Proc. Amer. Math. Soc. 90 (1984), 107-110
MSC: Primary 60F05; Secondary 60E15, 60G50
MathSciNet review: 722426
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Abstract: We derive a lower bound to the rate of convergence in the central limit theorem. Our result is expressed in terms similar to those of the Berry-Esséen inequality, with the distance between two distributions on one side of the inequality and an easily calculated function of the summands on the other, related by a universal constant. The proof is based on Stein's method.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0722426-X
Keywords: Berry-Esséen inequality, central limit theorem, lower bound, rate of convergence, sums of independent variables
Article copyright: © Copyright 1984 American Mathematical Society