Mathematics – Statistics Theory
Scientific paper
2006-07-03
Annals of Statistics 2006, Vol. 34, No. 2, 1013-1044
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/009053606000000164 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053606000000164
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.
Csorgo Miklós
Szyszkowicz Barbara
Wang Lihong
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