This article is cited in 3 papers

Short Communications

Nonclassical Error Bounds for Asymptotic Expansions in the Central Limit Theorem

L. S. Yaroslavtseva

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

Abstract: We present the first nonclassical error bound for short asymptotic expansions in the central limit theorem in $R$ for the case of independent but not necessarily identically distributed random variables. In the case of independent identically distributed random variables under the Cramér condition, this bound provides the correct order of convergence $(1/n)$, and the leading term in the bound is determined by powers of the third and fourth pseudomoments of the random summands.

Keywords: nonclassical error bound, pseudomoment, asymptotic expansions, central limit theorem.

Received: 16.05.2008

DOI: 10.4213/tvp2422

 English version: Theory of Probability and its Applications, 2009, 53:2, 365–367

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