Nonuniform Central Limit Bounds with Applications to Probabilities of Deviations
Michel, R.
Ann. Probab., Tome 4 (1976) no. 6, p. 102-106 / Harvested from Project Euclid
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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 $1 - F_n(t_n) = o(n^{-c/2}t_n^{2 + c})$.
Publié le : 1976-02-14
Classification:  Moment conditions,  approximation,  central limit theorem,  deviations,  60F99 
@article{1176996186,
     author = {Michel, R.},
     title = {Nonuniform Central Limit Bounds with Applications to Probabilities of Deviations},
     journal = {Ann. Probab.},
     volume = {4},
     number = {6},
     year = {1976},
     pages = { 102-106},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996186}
}

Michel, R. Nonuniform Central Limit Bounds with Applications to Probabilities of Deviations. Ann. Probab., Tome 4 (1976) no. 6, pp.  102-106. http://gdmltest.u-ga.fr/item/1176996186/