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Precise asymptotics in the law of the iterated logarithm and the complete convergence for uniform empirical process

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  • Zhang, Yong
  • Yang, Xiao-Yun

Abstract

Let {[xi]1,[xi]2,...,[xi]n} be a sequence of independent and identically distributed U[0,1]-distributed random variables. Define the uniform empirical process . For 1 =[epsilon]n1/p-1/2}, and as [epsilon]-->0.

Suggested Citation

  • Zhang, Yong & Yang, Xiao-Yun, 2008. "Precise asymptotics in the law of the iterated logarithm and the complete convergence for uniform empirical process," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1051-1055, July.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1051-1055
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    Cited by:

    1. Sergio Alvarez-Andrade & Salim Bouzebda, 2014. "Asymptotic results for hybrids of empirical and partial sums processes," Statistical Papers, Springer, vol. 55(4), pages 1121-1143, November.
    2. Fa-mei Zheng & Qing-pei Zang, 2015. "A general pattern of asymptotic behavior of the R/S statistics for linear processes," Statistical Papers, Springer, vol. 56(1), pages 191-204, February.
    3. Xiao, Xiao-Yong & Zhang, Li-Xin & Yin, Hong-Wei, 2013. "Precise rates in the generalized law of the iterated logarithm," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 616-623.

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