This article is cited in 2 papers

Nonimprovable estimates for asymptotic expansions in the central limit theorem

V. V. Senatov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

MSC: 60F05

Received: 15.11.2011

DOI: 10.4213/tvp4472

 English version: Theory of Probability and its Applications, 2013, 57:4, 633–648

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