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Siberian Mathematical Journal

, Volume 37, Issue 3, pp 447–453 | Cite as

On asymptotic expansion of the moments of smooth functions in the central limit theorem

  • I. S. Borisov
  • G. I. Skilyagina
Article
  • 27 Downloads

Keywords

Smooth Function Asymptotic Expansion Limit Theorem Central Limit Central Limit Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    B. Von Bahr, “On the convergence of moments in the central limit theorem,” Ann. Math. Statist.,36, No. 3, 808–818 (1965).Google Scholar
  2. 2.
    A. D. Barbour, “Asymptotic expansions based on smooth functions in the central limit theorem,” Probab. Theory. Related Fields,72, No. 2, 289–303 (1986).CrossRefGoogle Scholar
  3. 3.
    C. Hipp, “Edgeworth expansions for integrals of smooth functions,” Ann. Probab.,5, No. 6, 1004–1011 (1977).Google Scholar
  4. 4.
    V. V. Petrov, Sums of Independent Random Variables [in Russian], Nauka, Moscow (1972).Google Scholar
  5. 5.
    H. P. Rosenthal, “On the span inL p of sequences of independent random variables,” in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, 1972,2, pp. 149–167.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • I. S. Borisov
    • 1
  • G. I. Skilyagina
    • 1
  1. 1.Novosibirsk

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