The Annals of Probability

Nonuniform Central Limit Bounds with Applications to Probabilities of Deviations

R. Michel

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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 $1 - F_n(t_n) = o(n^{-c/2}t_n^{2 + c})$.

Article information

Source
Ann. Probab. Volume 4, Number 1 (1976), 102-106.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996186

Digital Object Identifier
doi:10.1214/aop/1176996186

Mathematical Reviews number (MathSciNet)
MR391226

Zentralblatt MATH identifier
0337.60026

JSTOR
links.jstor.org

Subjects
Primary: 60F99: None of the above, but in this section

Keywords
Moment conditions approximation central limit theorem deviations

Citation

Michel, R. Nonuniform Central Limit Bounds with Applications to Probabilities of Deviations. Ann. Probab. 4 (1976), no. 1, 102--106. doi:10.1214/aop/1176996186. https://projecteuclid.org/euclid.aop/1176996186


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