论文标题
序数模式依赖性作为多元依赖度量
Ordinal pattern dependence as a multivariate dependence measure
论文作者
论文摘要
在本文中，我们表明，最近引入的序数模式依赖关系符合一般多元依赖度量的公理框架，即两个多变量随机对象之间的依赖度量。此外，我们考虑了诸如Kendall的$τ$，Spearman的$ρ$和Pearson的相关系数之类的已建立单变量依赖度量的多元概括。其中，只有多元Kendall的$τ$证明是将来自多维时间序列的随机向量的动态依赖性所考虑的。因此，本文的重点是在这种情况下对序数模式依赖性和多元肯德尔的$τ$进行比较。为此，在近类依赖的数据生成时间序列的假设下建立了多元肯德尔的$τ$的限制定理。我们分析了如何与多元肯德尔的$τ$和皮尔逊的相关系数相比，在理论上。此外，一项仿真研究说明了多变量Kendall的$τ$和序数模式依赖性所揭示的依赖性的差异。
In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures, i.e., measures of dependence between two multivariate random objects. Furthermore, we consider multivariate generalizations of established univariate dependence measures like Kendall's $τ$, Spearman's $ρ$ and Pearson's correlation coefficient. Among these, only multivariate Kendall's $τ$ proves to take the dynamical dependence of random vectors stemming from multidimensional time series into account. Consequently, the article focuses on a comparison of ordinal pattern dependence and multivariate Kendall's $τ$ in this context. To this end, limit theorems for multivariate Kendall's $τ$ are established under the assumption of near-epoch dependent data-generating time series. We analyze how ordinal pattern dependence compares to multivariate Kendall's $τ$ and Pearson's correlation coefficient on theoretical grounds. Additionally, a simulation study illustrates differences in the kind of dependencies that are revealed by multivariate Kendall's $τ$ and ordinal pattern dependence.
