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