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)
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.
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Publisher Info
Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number
lrsp-TRS387.
Length: 34 pages Date of creation: 01 Jan 2000 Date of revision: Handle: RePEc:pqs:wpaper:0152005
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Find related papers by JEL classification: C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General