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

• 成果类型: Article
• 署名作者: Csorgo, Miklos; Kulik, Rafal
• 署名单位: University of Sydney; Carleton University; University of Wroclaw
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0107-9
• 发表日期: 2008
• 页码: 339-366
• 关键词: memory moving averages; Empirical Processes; stable limits; variance

摘要

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.