Pointwise and uniform asymptotics of the Vervaat error process

Endre Csáki, Miklós Csörgo, Antónia Földes, Zhan Shi, Ričardas Zitikis

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4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)845-875
Number of pages31
JournalJournal of Theoretical Probability
Volume15
Issue number4
DOIs
Publication statusPublished - Dec 1 2002

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Keywords

  • Bahadur Kiefer process
  • Brownian bridge
  • Convergence in distribution.
  • Empirical process
  • Kiefer process
  • Law of the iterated logarithm
  • Quantile process
  • Strong approximation
  • Vervaat error process
  • Vervaat process
  • Wiener process

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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