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Pointwise and Uniform Asymptotics of the Vervaat Error Process

Author

Listed:
  • Endre Csáki

    (Alfréd Rényi Institute of Mathematics)

  • Miklós Csörgő

    (Carleton University)

  • Antónia Földes

    (City University of New York)

  • Zhan Shi

    (Université Paris VI)

  • Ričardas Zitikis

    (The University of Western Ontario)

Abstract

It is well known that, asymptotically, the appropriately normalized uniform Vervaat process, i.e., the integrated uniform Bahadur–Kiefer process properly normalized, behaves like the square of the uniform empirical process. We give a complete description of the strong and weak asymptotic behaviour in sup-norm of this representation of the Vervaat process and, likewise, we also study its pointwise asymptotic behaviour.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:4:d:10.1023_a:1020650502619
    DOI: 10.1023/A:1020650502619
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    References listed on IDEAS

    as
    1. Csörgo, Miklós & Zitikis, Ricardas, 1996. "Strassen's LIL for the Lorenz Curve," Journal of Multivariate Analysis, Elsevier, vol. 59(1), pages 1-12, October.
    2. Paul Deheuvels, 1998. "On the Approximation of Quantile Processes by Kiefer Processes," Journal of Theoretical Probability, Springer, vol. 11(4), pages 997-1018, October.
    3. Csörgo, Miklós & Zitikis, Ricardas, 2001. "The Vervaat Process in Lp Spaces," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 103-138, July.
    4. Einmahl, J.H.J., 1996. "A short and elementary proof of the main Bahadur-Kiefer theorem," Other publications TiSEM bd980f38-c118-4174-9816-8, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Miklós Csörgő & Rafał Kulik, 2008. "Weak Convergence of Vervaat and Vervaat Error Processes of Long-Range Dependent Sequences," Journal of Theoretical Probability, Springer, vol. 21(3), pages 672-686, September.

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