Non-parametric tests for cross-dependence based on multivariate extensions of ordinal patterns
本文提出基于序数模式及其多元推广的交叉依赖非参数检验方法，推导检验统计量的极限分布，通过模拟比较其与Pearson、Spearman和Chatterjee相关系数的性能，并用两个真实数据示例展示应用。
Analyzing the cross-dependence within sequentially observed pairs of random variables is an interesting mathematical problem that also has several practical applications. Most of the time, classical dependence measures like Pearson's correlation are used to this end. This quantity, however, only measures linear dependence and has other drawbacks as well. Different concepts for measuring cross-dependence in sequentially observed random vectors, which are based on so-called ordinal patterns or multivariate generalizations of them, are described. In all cases, limiting distributions of the corresponding test statistics are derived. In a simulation study, the performance of these statistics is compared with three competitors, namely, classical Pearson's and Spearman's correlation as well as the rank-based Chatterjee's correlation coefficient . The applicability of the test statistics is illustrated by using them on two real-world data examples.