论文标题
基于经验的高维度测试高维度的独立性
Testing for independence in high dimensions based on empirical copulas
论文作者
论文摘要
在近年来，对变量数量可能相同甚至大于样本量相同甚至大的情况，对成对独立性的测试。我们通过考虑允许检测高阶依赖性的测试来为文献的这一分支做出贡献。所提出的方法基于将问题与Copulas联系起来，并利用经验副群的Moebius转换。已成功用于固定变量数量的情况。基于Martingale Central Limit定理，可以表明各个测试统计量会收敛到标准正态分布，从而可以直接定义临界值。结果通过蒙特卡洛模拟研究说明了结果。
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 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.
