Geodesic
Nonimprovable estimates for asymptotic expansions in the central limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 649-666

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We obtain new asymptotic expansions in the central limit theorem with explicit estimates of the approximation accuracy, which are guaranteed by the expansions. For some of these estimates the statement about their nonimprovability is valid.
Keywords: central limit theorem; asymptotic expansions; accuracy of approximation. 
@article{TVP_2012_57_4_a1,
     author = {V. V. Senatov},
     title = {Nonimprovable estimates for asymptotic expansions in the central limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {649--666},
     publisher = {mathdoc},
     volume = {57},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a1/}
}
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V. V. Senatov. Nonimprovable estimates for asymptotic expansions in the central limit theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 649-666. http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a1/