In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These tests are derived from copula-based covariances and their multivariate extensions using M\"obius transforms. We find the asymptotic distributions of the statistics under the null hypothesis of independence or randomness, as well as under contiguous alternatives. This enables us to find out locally most powerful test statistics for some alternatives, whatever the margins. Numerical experiments are performed for Wald's type combinations of these statistics to assess the finite sample performance.

翻译：本文研究了非序列情形下（即独立同分布随机向量）以及序列情形下（即时间序列）具有任意分布数据的独立性检验。这些检验基于copula协方差及其通过Möbius变换得到的多元扩展。我们推导了在原假设（独立性或随机性）以及邻接备择假设下统计量的渐近分布，从而能够针对某些备择假设（无论边际分布如何）找出局部最优势检验统计量。通过数值实验对Wald型组合统计量进行有限样本性能评估。