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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Reversing the Berry-Esseen inequality
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by Peter Hall and A. D. Barbour PDF
Proc. Amer. Math. Soc. 90 (1984), 107-110 Request permission

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
  • © Copyright 1984 American Mathematical Society
  • 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