Testing for independence in high dimensions based on empirical copulas
针对变量数可能等于或大于样本量的高维情形，提出基于经验连接函数和莫比乌斯变换的检验方法，可检测高阶依赖关系，并证明检验统计量收敛到标准正态分布。
Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature by considering tests that allow to detect higher-order dependencies. The proposed methods are based on connecting the problem to copulas and making use of the Moebius transformation of the empirical copula process; an approach that is related to Lancaster interactions and that has already been used successfully for the case where the number of variables is fixed. Based on a martingale central limit theorem, it is shown that respective test statistics converge to the standard normal distribution, allowing for straightforward definition of critical values. The results are illustrated by a Monte Carlo simulation study.