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April 2006 Strong invariance principles for sequential Bahadur–Kiefer and Vervaat error processes of long-range dependent sequences
Miklós Csörgő, Barbara Szyszkowicz, Lihong Wang
Ann. Statist. 34(2): 1013-1044 (April 2006). DOI: 10.1214/009053606000000164

Abstract

In this paper we study strong approximations (invariance principles) of the sequential uniform and general Bahadur–Kiefer processes of long-range dependent sequences. We also investigate the strong and weak asymptotic behavior of the sequential Vervaat process, that is, the integrated sequential Bahadur–Kiefer process, properly normalized, as well as that of its deviation from its limiting process, the so-called Vervaat error process. It is well known that the Bahadur–Kiefer and the Vervaat error processes cannot converge weakly in the i.i.d. case. In contrast to this, we conclude that the Bahadur–Kiefer and Vervaat error processes, as well as their sequential versions, do converge weakly to a Dehling–Taqqu type limit process for certain long-range dependent sequences.

Citation

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Miklós Csörgő. Barbara Szyszkowicz. Lihong Wang. "Strong invariance principles for sequential Bahadur–Kiefer and Vervaat error processes of long-range dependent sequences." Ann. Statist. 34 (2) 1013 - 1044, April 2006. https://doi.org/10.1214/009053606000000164

Information

Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1113.60034
MathSciNet: MR2283402
Digital Object Identifier: 10.1214/009053606000000164

Subjects:
Primary: 60F15 , 60F17
Secondary: 60G10 , 60G18

Keywords: long-range dependence , sequential Bahadur–Kiefer process , sequential empirical and quantile processes , sequential Vervaat and Vervaat error processes , Strong invariance principles

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 2 • April 2006
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