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Asymptotic expansions based on smooth functions in the central limit theorem
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  • Published: June 1986

Asymptotic expansions based on smooth functions in the central limit theorem

  • A. D. Barbour1 

Probability Theory and Related Fields volume 72, pages 289–303 (1986)Cite this article

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Summary

Stein's method is used to derive asymptotic expansions for expectations of smooth functions of sums of independent random variables, together with Lyapounov estimates of the error in the approximation.

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References

  • von Bahr, B.: On the convergence of moments in the central limit theorem. Ann. Math. Statist.36, 808–818 (1965)

    Google Scholar 

  • Bhattacharya, R.N.: Recent results on refinements of the central limit theorem. Proc. VI th Berkeley Sympos. Math. Statist. Probab.2, 453–484 (1970)

    Google Scholar 

  • Götze, F., Hipp, C.: Asymptotic expansions in the central limit theorem under moment conditions. Z. Wahrscheinlickeistheor. Verw. Geb.42, 67–87 (1978)

    Google Scholar 

  • Hipp, C.: Edgeworth expansions for integrals of smooth functions. Ann. Probab.5, 1004–1011 (1977)

    Google Scholar 

  • Hsu, P.L.: The approximate distribution of the mean and variance of a sample of independent variables. Ann. Math. Statist.16, 1–29 (1945)

    Google Scholar 

  • Marcinkiewicz, J., Zygmund, A.: Sur les fonctions indépendantes. Fundam. Math.29, 60–90 (1937)

    Google Scholar 

  • Stein, C.: A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proc. VIth Berkeley Sympos. Math. Statist. Probab.2, 583–602 (1970)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Zürich, CH-8001, Zürich, Switzerland

    A. D. Barbour

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  1. A. D. Barbour
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Cite this article

Barbour, A.D. Asymptotic expansions based on smooth functions in the central limit theorem. Probab. Th. Rel. Fields 72, 289–303 (1986). https://doi.org/10.1007/BF00699108

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  • Received: 25 November 1984

  • Issue Date: June 1986

  • DOI: https://doi.org/10.1007/BF00699108

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Keywords

  • Stochastic Process
  • Stein
  • Smooth Function
  • Probability Theory
  • Asymptotic Expansion
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