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

DOI:
https://doi.org/10.1090/S0002-9939-1984-0722426-X

MathSciNet review:
722426

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

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