On the dependence structure of order statistics
On the dependence structure of order statistics
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DOI：
10.1016/j.jmva.2004.03.004
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发表时间：
2005-05
影响因子：
1.6
通讯作者：
J. Avérous;C. Genest;S. Kochar
中科院分区：
文献类型：
--
作者：
J. Avérous;C. Genest;S. Kochar
给定一个连续变量的随机样本，我们观察到连接任意一对序统计量的联结是独立于母分布的。为了比较两个这样的有序随机变量对之间的关联程度，考虑了相对单调回归依赖（或随机增加）的概念。利用这一概念，证明了当i<j时，随着i和j的分离，第j阶统计量对第i阶统计量的依赖性减小。这扩展了Tukey (Ann。数学。统计学家，29(1958)588)和金和大卫(J.统计学家。Plann。推理24(1990)363)。本文还研究了样本量对这种依赖的影响，并给出了随机样本的两个任意阶统计量之间的肯德尔协调系数的总体值的显式表达式。
Given a random sample from a continuous variable, it is observed that the copula linking any pair of order statistics is independent of the parent distribution. To compare the degree of association between two such pairs of ordered random variables, a notion of relative monotone regression dependence (or stochastic increasingness) is considered. Using this concept, it is proved that for i<j, the dependence of the jth order statistic on the ith order statistic decreases as i and j draw apart. This extends earlier results of Tukey (Ann. Math. Statist. 29 (1958) 588) and Kim and David (J. Statist. Plann. Inference 24 (1990) 363). The effect of the sample size on this type of dependence is also investigated, and an explicit expression is given for the population value of Kendall's coefficient of concordance between two arbitrary order statistics of a random sample.