Geodesic
Sharpening of the upper-estimate of the absolute constant in the Berry--Esseen inequality
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 622-626

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The upper bound of the absolute constant in the classical Berry–Esseen inequality for sums of independent identically distributed random variables with finite third moments is lowered to $C\leqslant 0.7056$.
Keywords: Berry–Esseen inequality, central limit theorem, normal approximation, convergence rate estimate. 
@article{TVP_2006_51_3_a13,
     author = {I. G. Shevtsova},
     title = {Sharpening of the upper-estimate of the absolute constant in the {Berry--Esseen} inequality},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {622--626},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a13/}
}
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I. G. Shevtsova. Sharpening of the upper-estimate of the absolute constant in the Berry--Esseen inequality. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 622-626. http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a13/