Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs
Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs
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DOI：
10.1080/01621459.2020.1782223
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发表时间：
2019-09
影响因子：
3.7
通讯作者：
Hongjian Shi;M. Drton;Fang Han
中科院分区：
文献类型：
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作者：
Hongjian Shi;M. Drton;Fang Han
摘要 本文研究了测试两个一般维度的随机向量的独立性的问题。为此，我们首次给出了无分布的一致性测试。我们的方法将距离协方差与 Marc Hallin 及其合作者开发的中心向外排名和符号相结合。用技术术语来说，所提出的检验在具有非零（勒贝格）概率密度的多元分布族中是一致的且无分布的。利用距离协方差的（简并）U 统计结构以及 Hallin 的中心向外秩和符号的组合性质，我们能够导出检验统计量的极限零分布。对于中等样本量，所得的渐近近似已经是准确的，并且使得测试可以在不需要排列的情况下实施。极限分布是通过更一般的结果导出的，该结果给出了双索引和多索引排列统计的新型组合非中心极限定理。本文的补充材料可在线获取。
Abstract This article investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the center-outward ranks and signs developed by Marc Hallin and collaborators. In technical terms, the proposed test is consistent and distribution-free in the family of multivariate distributions with nonvanishing (Lebesgue) probability densities. Exploiting the (degenerate) U-statistic structure of the distance covariance and the combinatorial nature of Hallin’s center-outward ranks and signs, we are able to derive the limiting null distribution of our test statistic. The resulting asymptotic approximation is accurate already for moderate sample sizes and makes the test implementable without requiring permutation. The limiting distribution is derived via a more general result that gives a new type of combinatorial noncentral limit theorem for double- and multiple-indexed permutation statistics. Supplementary materials for this article are available online.