On the Bahadur representation of sample quantiles for sequences of φ-mixing random variables
On the Bahadur representation of sample quantiles for sequences of φ-mixing random variables
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DOI：
10.1016/0047-259x(72)90011-5
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发表时间：
1972-03
影响因子：
1.6
通讯作者：
P. Sen
中科院分区：
文献类型：
--
作者：
P. Sen
本研究的目的是证明由 Bahadur [1] 建立的独立同分布随机变量样本分位数的优雅渐近几乎确定表示对于 φ 混合随机变量的平稳序列成立。在不同的 φ 混合条件下，获得了两个不同阶的余项，并将其用于证明样本分位数的两个函数中心极限定理。还表明，迭代对数定律对于平稳 φ 混合过程中的分位数成立。
The object of the present investigation is to show that the elegant asymptotic almost-sure representation of a sample quantile for independent and identically distributed random variables, established by Bahadur [1] holds for a stationary sequence of φ-mixing random variables. Two different orders of the remainder term, under different φ-mixing conditions, are obtained and used for proving two functional central limit theorems for sample quantiles. It is also shown that the law of iterated logarithm holds for quantiles in stationary φ-mixing processes.