Reduction principles for quantile and Bahadur-Kiefer processes of long-range dependent linear sequences

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dc.creatorCsörgő, Miklós
dc.creatorKulik, Rafal
dc.date2008-02-07
dc.date.accessioned2026-07-07T09:19:18Z
dc.date.available2026-07-07T09:19:18Z
dc.descriptionIn this paper we consider quantile and Bahadur-Kiefer processes for long range dependent linear sequences. These processes, unlike in previous studies, are considered on the whole interval $(0,1)$. As it is well-known, quantile processes can have very erratic behavior on the tails. We overcome this problem by considering these processes with appropriate weight functions. In this way we conclude strong approximations that yield some remarkable phenomena that are not shared with i.i.d. sequences, including weak convergence of the Bahadur-Kiefer processes, a different pointwise behavior of the general and uniform Bahadur-Kiefer processes, and a somewhat "strange" behavior of the general quantile process.
dc.descriptionPreprint. The final version will appear in Probability Theory and Related Fields
dc.identifierhttps://arxiv.org/abs/0802.1025
dc.identifierhttp://arxiv.org/abs/0802.1025
dc.identifierdoi:10.1007/s00440-007-0107-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154339
dc.subjectStatistics Theory
dc.titleReduction principles for quantile and Bahadur-Kiefer processes of long-range dependent linear sequences
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