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February, 1976 Nonuniform Central Limit Bounds with Applications to Probabilities of Deviations
R. Michel
Ann. Probab. 4(1): 102-106 (February, 1976). DOI: 10.1214/aop/1176996186

Abstract

For the distribution of the standardized sum of independent and identically distributed random variables, nonuniform central limit bounds are proved under an appropriate moment condition. From these theorems a condition on the sequence $t_n, n \in \mathbb{N}$, is derived which implies that $1 - F_n(t_n)$ is equivalent to the corresponding deviation of a normally distributed random variable. Furthermore, a necessary and sufficient condition is given for $1 - F_n(t_n) = o(n^{-c/2}t_n^{2 + c})$.

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R. Michel. "Nonuniform Central Limit Bounds with Applications to Probabilities of Deviations." Ann. Probab. 4 (1) 102 - 106, February, 1976. https://doi.org/10.1214/aop/1176996186

Information

Published: February, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0337.60026
MathSciNet: MR391226
Digital Object Identifier: 10.1214/aop/1176996186

Subjects:
Primary: 60F99

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 1 • February, 1976
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