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

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• 作者：Mikl¨®s Cs?rg? and Rafa? Kulik
• 关键词：Long range dependence ; Linear processes ; Bahadur&#8211 ; Kiefer process ; Quantile processes ; Strong approximation
• 刊名：Probability Theory and Related Fields
• 出版年：2008
• 出版时间：November, 2008
• 年：2008
• 卷：142
• 期：3-4
• 页码：339-366
• 全文大小：328.9 KB

文摘

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.