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Applied Mathematics and Mechanics

, Volume 17, Issue 8, pp 741–750 | Cite as

The law of the iterated logarithm of random weighting approximation for mean error—Non. I. I. D. situation

  • Wang Bingzhang
  • Peng Jianping
Article
  • 10 Downloads

Abstract

For the distribution of mean error under independent but not identically distributed conditions, its approximating distribution whose precision reach \(O(\sqrt {1n1nn} /n\) is obtained.

Key words

mean error random weight approximation 

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References

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    TuDongsheng and ZhengZongguo, Asymptotic expansion of random weighting method, The Chinese Journal of Applied Probability and Statistics, 3, 4 (1987), 340–347. (in Chinese)Google Scholar
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    Bai Zhidong ahd Zhao Lincheng, Asymptotic expansion of the distribution of the sum of independent random variables, Scientia Sinica, 8 (1985). (in Chinese)Google Scholar
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    V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag (1975).Google Scholar
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    YaoZeqing, Approximation to distributions admitting edgeworth expansion, Journal of Systems Science and Mathematical Sciences, 8, 2 (1988), 113–126. (in Chinese)Google Scholar
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    R.Wittmann, A general law of iterated logarithm, Z. Wahr. Verw. Geb., 68 (1985), 521–543.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Wang Bingzhang
    • 1
  • Peng Jianping
    • 1
  1. 1.Yantai UniversityYantaiP. R. China

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