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摘要翻译：
本文研究了长程相依线性序列的分位数和Bahadur-Kiefer过程。与以往的研究不同，这些过程是在整个区间$(0,1)$上考虑的。众所周知，分位数过程在尾部可能有非常不稳定的行为。我们通过用适当的权函数考虑这些过程来克服这个问题。通过这种方式，我们得出了强近似，产生了一些与I.I.D.不相同的显著现象。序列，包括Bahadur-Kiefer过程的弱收敛性，一般和一致Bahadur-Kiefer过程的不同点态行为，以及一般分位数过程的有点“奇怪”的行为。
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英文标题：
《Reduction principles for quantile and Bahadur-Kiefer processes of
long-range dependent linear sequences》
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作者：
Mikl\'os Cs\"org\H{o} and Rafal Kulik
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/802.1025
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