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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the rate of convergence of moments in the central limit theorem for lattice distributions
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by Peter Hall PDF
Trans. Amer. Math. Soc. 278 (1983), 169-181 Request permission

Abstract:

We derive sharp asymptotic expressions for moments of the type $E\{ b(|{S_n}/{n^{1/2}}|)\}$, 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.
References
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 278 (1983), 169-181
  • MSC: Primary 60F05
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0697068-9
  • MathSciNet review: 697068