Strong invariance principles for sequential Bahadur-Kiefer and Vervaat error processes of long-range dependent sequences

Miklos Csorgo, Barbara Szyszkowicz and Lihong Wang
Additional contact information
Miklos Csorgo: School of Mathematics and Statistics, Carleton University
Barbara Szyszkowicz: School of Mathematics and Statistics, Carleton University
Lihong Wang: Department of Mathematics, Nanjing University

No lrsp-TRS387, RePAd Working Paper Series from Département des sciences administratives, UQO

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, i.e., 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.

Keywords: Long-range dependence; Sequential empirical and quantile processes; Sequential Bahadur-Kiefer process; Sequential Vervaat and Vervaat error processes; Strong invariance principles. (search for similar items in EconPapers)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Date: 2000-01-01

Downloads: (external link)
http://www.repad.org/ca/on/lrsp/TRS387.pdf First version, 2000 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:pqs:wpaper:0152005

Access Statistics for this paper

More papers in RePAd Working Paper Series from Département des sciences administratives, UQO
Contact information at EDIRC.
Series data maintained by Christian Calmes ().