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Nonuniform error bounds in asymptotic expansions for scale mixtures under mild moment conditions

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Abstract

Let F(x) be a distribution function of of a scale mixture X=SZ of a random variable Z with distribution G and scale factor S, which is a positive random variable independent of Z. Some nonuniform bounds are given for asymptotic expansions of F(x) around G(x)_ under mild moment conditions on the distribution of S. Some nonuniform bounds for the normal approximation to the Student t-distribution are given as examples.

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References

  1. Y. Fujikoshi, “Error bounds for asymptotic approximations of some distribution functions,” in:Multivariate Analysis: Future Directions, Elsevier (1993), pp. 181–208.

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Authors and Affiliations

  1. Moscow State University, Vorob'yovy Gory, 119899, Moscow, Russia

    V. Ulyanov

  2. Hiroshima University, Higashi-Hiroshima, Japan

    Y. Fujikoshi

  3. The Institute of Statistical Mathematics, Tokyo, Japan

    R. Shimizu

Authors
  1. V. Ulyanov
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  2. Y. Fujikoshi
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  3. R. Shimizu
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Additional information

Supported by a Grant-in-Aid for the COE Research Program, The Minsitry of Education, Science, Sports, and Culture, Japan, and by the Russian Foundation for Fundamental Research (grant No. 96-01-01919).

Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997. Part III.

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Ulyanov, V., Fujikoshi, Y. & Shimizu, R. Nonuniform error bounds in asymptotic expansions for scale mixtures under mild moment conditions. J Math Sci 93, 600–608 (1999). https://doi.org/10.1007/BF02365066

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  • DOI: https://doi.org/10.1007/BF02365066

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