Geodesic
Nonimprovable estimates for asymptotic expansions in the central limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 649-666 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {V. V. Senatov},
     title = {Nonimprovable estimates for asymptotic expansions in the central limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     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/

[1] Senatov V. V., Tsentralnaya predelnaya teorema: Tochnost approksimatsii i asimptoticheskie razlozheniya, Knizhnyi dom “Librokom”, M., 2009, 352 pp.

[2] Senatov V. V., Sobolev V. N., “O novykh formakh asimptoticheskikh razlozhenii v tsentralnoi predelnoi teoreme”, Teoriya veroyatn. i ee primen., 57:1 (2012), 124–140