Over the last few decades, various copula‐based methods have been proposed in the literature for testing independence among several random variables. But most of these tests are applicable only when all random variables are continuous. Only recently, a copula‐based test of independence has been proposed, which also works for random variables having arbitrary probability distributions. But like most of the existing methods, this test is not invariant under monotone transformations of the variables unless the same type of transformation (either increasing or decreasing) is used for all variables. Moreover, it often yields poor results when these variables have complex non‐monotone relationships. In this article, we propose some copula‐based tests of independence, which take care of this problem. Our tests are invariant under strictly monotone transformations of the variables, and they can be used for continuous, discrete, or even for ordinal variables. We establish the large sample consistency of these tests under appropriate regularity conditions. Several simulated and real data sets are analysed to compare their empirical performance with some popular tests.

中文翻译：

---

在某些具有任意概率分布的随机变量之间进行的基于copula的独立性检验

在过去的几十年中，文献中提出了各种基于copula的方法来测试几个随机变量之间的独立性。但是，只有当所有随机变量都是连续的时，这些测试中的大多数才适用。直到最近，才提出了基于copula的独立性测试，该测试也适用于具有任意概率分布的随机变量。但是，与大多数现有方法一样，除非对所有变量使用相同类型的转换（递增或递减），否则该测试在变量的单调变换下不会不变。此外，当这些变量具有复杂的非单调关系时，通常会产生较差的结果。在本文中，我们提出了一些基于copula的独立性测试，可以解决此问题。在严格的变量单调变换下，我们的测试是不变的，它们可以用于连续变量，离散变量甚至有序变量。我们在适当的规律性条件下建立了这些测试的大样本一致性。分析了几个模拟数据集和实际数据集，以将其经验性能与一些流行的测试进行比较。