Rate-Optimality of Consistent Distribution-Free Tests of Independence Based on Center-Outward Ranks and Signs
Rate-Optimality of Consistent Distribution-Free Tests of Independence Based on Center-Outward Ranks and Signs
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基于中心向外排序和符号的一致无分布独立性检验的速率最优性
DOI：
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Fang Han
中科院分区：
文献类型：
--
作者：
Hongjian Shi;M. Hallin;M. Drton;Fang Han
在过去的十年里，等级相关性已经发现了许多创新的应用。特别是，等级相关性的适当版本已被用于对随机变量对之间的独立性的一致性测试。随着测试变得不需要分布，对于连续数据来说，使用秩次尤其有吸引力。然而，传统的排名概念依赖于排序数据，因此与单变量观测相联系。因此，人们长期以来一直不清楚如何构造多变量随机向量之间无分布但一致的独立性检验。这就是我们在本文中解决的问题，在本文中，我们设计了一个通用的框架，用于设计相关性度量，这些度量给出的多元独立性检验不仅是一致的和无分布的，而且我们还证明了它在统计上是有效的。我们的框架利用了最近引入的中心-外向等级和符号的概念，这是对传统等级的多变量概括，并采用了一种通用的标准形式来衡量依赖程度，其中包含了文献中的许多流行衡量标准。在统一的研究中，我们得到了独立条件下中心向外检验统计量的一般渐近表示，并将经典的Hajek渐近表示结果推广到多元情形。该表示法允许直接计算所建议的测试统计量的极限零分布。此外，通过首次建立Konijn备择方案家族内中心向外检验的最优率，它促进了局部力量分析，从而为多变量等级的中心向外方法提供了强有力的支持。
Rank correlations have found many innovative applications in the last decade. In particular,suitable versions of rank correlations have been used for consistent tests of independence between pairs of random variables. The use of ranks is especially appealing for continuous data as tests become distribution-free. However, the traditional concept of ranks relies on ordering data and is, thus, tied to univariate observations. As a result it has long remained unclear how one may construct distribution-free yet consistent tests of independence between multivariate random vectors. This is the problem we address in this paper, in which we lay out a general framework for designing dependence measures that give tests of multivariate independence that are not only consistent and distribution-free but which we also prove to be statistically efficient. Our framework leverages the recently introduced concept of center-outward ranks and signs, a multivariate generalization of traditional ranks, and adopts a common standard form for dependence measures that encompasses many popular measures from the literature. In a unified study, we derive a general asymptotic representation of center-outward test statistics under independence, extending to the multivariate setting the classical Hajek asymptotic representation results. This representation permits a direct calculation of limiting null distributions for the proposed test statistics. Moreover, it facilitates a local power analysis that provides strong support for the center-outward approach to multivariate ranks by establishing, for the first time, the rate-optimality of center-outward tests within families of Konijn alternatives.
影响因子：
2.7
作者：
Weihs, L.;Drton, M.;Meinshausen, N.
通讯作者：
Meinshausen, N.
DOI：
10.1080/01621459.2021.1923508
发表时间：
2021-06-16
影响因子：
3.7
作者：
Deb，Nabarun;Sen，Bodhisattva
通讯作者：
Sen，Bodhisattva
影响因子：
0.9
作者：
Heller, R.;Gorfine, M.;Heller, Y.
通讯作者：
Heller, Y.