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Reversing the Berry-Esséen Inequality

Peter Hall and A. D. Barbour
Proceedings of the American Mathematical Society
Vol. 90, No. 1 (Jan., 1984), pp. 107-110
DOI: 10.2307/2044679
Stable URL: http://www.jstor.org/stable/2044679
Page Count: 4
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Reversing the Berry-Esséen Inequality
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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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