We present novel tests for the hypothesis of independence when the number of variables is larger than the number of vector observations. We show that two multivariate normal vectors are independent if and only if their interpoint distance are independent. The proposed test statistics exploit different properties of the sample interpoint distances. A simulation study compares the new tests with three existing tests under various scenarios, including monotone and non-monotone dependence structures. Numerical results show that the new methods are effective for independence testing.

中文翻译：

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基于点间距离的非参数独立性检验

当变量的数量大于向量观察的数量时，我们对独立性假设提出了新的检验。我们证明两个多元法向量是独立的，当且仅当它们的点间距离是独立的。建议的测试统计利用样本点间距离的不同特性。一项模拟研究将新测试与不同场景下的三个现有测试进行了比较，包括单调和非单调依赖结构。数值结果表明，新方法对独立性测试是有效的。