Geodesic
An estimate of the concentration function by the Esseen method
Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 3, pp. 561-577

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The paper deals with the Esseen method of obtaining upper estimates for the concentration function of a random variable $X$ in terms of the characteristic function of $X$. Some problems of the parametric optimization of such estimates are solved. Applications are described to the estimation of the probabilities of large deviations of the sums of identically distributed random variables.
Keywords: concentration function, characteristic function, probabilities of large deviations, Esseen inequality, Euler numbers.
Mots-clés : Poisson summation formula 
@article{TVP_1996_41_3_a4,
     author = {N. P. Salikhov},
     title = {An estimate of the concentration function by the {Esseen} method},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {561--577},
     publisher = {mathdoc},
     volume = {41},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1996_41_3_a4/}
}
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N. P. Salikhov. An estimate of the concentration function by the Esseen method. Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 3, pp. 561-577. http://geodesic.mathdoc.fr/item/TVP_1996_41_3_a4/