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On the Approximation of Quantile Processes by Kiefer Processes

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  • Paul Deheuvels

Abstract

We prove that the best possible almost sure rate of uniform approximation of a uniform quantile process by a normed Kiefer process is O(n −1/4(log n)1/2× (log log n)1/4).

Suggested Citation

  • Paul Deheuvels, 1998. "On the Approximation of Quantile Processes by Kiefer Processes," Journal of Theoretical Probability, Springer, vol. 11(4), pages 997-1018, October.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:4:d:10.1023_a:1022668932637
    DOI: 10.1023/A:1022668932637
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    References listed on IDEAS

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    1. Mason, David M., 1984. "A strong limit theorem for the oscillation modulus of the uniform empirical quantile process," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 127-136, May.
    2. Deheuvels, Paul, 1992. "Functional laws of the iterated logarithm for large increments of empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 133-163, November.
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    Cited by:

    1. Endre Csáki & Miklós Csörgő & Antónia Földes & Zhan Shi & Ričardas Zitikis, 2002. "Pointwise and Uniform Asymptotics of the Vervaat Error Process," Journal of Theoretical Probability, Springer, vol. 15(4), pages 845-875, October.

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