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Transactions of the American Mathematical Society

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On the rate of convergence of moments in the central limit theorem for lattice distributions


Author: Peter Hall
Journal: Trans. Amer. Math. Soc. 278 (1983), 169-181
MSC: Primary 60F05
MathSciNet review: 697068
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Abstract: We derive sharp asymptotic expressions for moments of the type $ E\{ b(\vert{S_n}/{n^{1/2}}\vert)\} $, where $ {S_n}$ is a sum of independent lattice-valued random variables with finite variance, and $ b$ is a concave function. It is shown that the behaviour of $ b$ at the origin has a profound effect on the behaviour of such moments, and that this influence accounts for the major difference between the properties of moments of lattice and nonlattice sums. Asymptotic expansions for moments of sums of lattice-valued variables are also derived.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0697068-9
Keywords: Asymptotic expansion, lattice-valued variable, moments, rate of convergence
Article copyright: © Copyright 1983 American Mathematical Society