We introduce a new dependence order that satisfies eight natural axioms that we propose for a global dependence order. Its minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information monotonicity, and exhibits several invariance properties. Consequently,it is an ordering for the strength of functional dependence of a random variable Y on a random vector X. As we show, various dependence measures, such as Chatterjee's rank correlation, are increasing in this order. We characterize our ordering by the Schur order and by the concordance order, and we verify it in models such as the additive error model, the multivariate normal distribution, and various copula-based models.

翻译：我们提出了一种新的依赖序，该序满足我们为全局依赖序提出的八条自然公理。其最小元与最大元分别刻画了独立性与完全依赖性。此外，该序能够表征条件独立性，满足信息单调性，并具有多种不变性性质。因此，它构成了随机变量Y对随机向量X的函数依赖强度的序关系。如我们所证，多种依赖度量（例如Chatterjee秩相关系数）在此序下是单调递增的。我们通过Schur序与一致性序刻画了该序关系，并在加性误差模型、多元正态分布及多种基于Copula的模型中验证了其有效性。