Mathematics – Statistics Theory
Scientific paper
2008-02-07
Mathematics
Statistics Theory
Preprint. The final version will appear in Probability Theory and Related Fields
Scientific paper
10.1007/s00440-007-0107-9
In 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.
Csorgo Miklós
Kulik Rafal
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