On universally consistent and fully distribution-free rank tests of vector independence
随机向量独立性的普遍一致、完全分布自由秩检验AI 解读 ↓
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随机向量独立性的普遍一致、完全分布自由秩检验
- 研究问题
- 传统秩依赖一维排序，如何为随机向量构造既分布自由又一致的独立性检验，并分析其局部备择下的检验能力？
- 方法与思路
- 作者利用由中心向外的秩与符号及统一形式的依赖度量，建立多元秩统计量渐近表示，以推导零分布并分析局部功效。
- 材料陈述的贡献
- 摘要称框架给出一致且分布自由的检验，并在二次均值可微备择的根号 n 局部邻域中证明非平凡功效及效率性质。
- 阅读关注点
- 应核对分布自由性和普遍一致性的条件、依赖度量的覆盖范围，以及局部功效与统计效率结论采用的具体定义。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；条件、效率基准与计算实现未提供，不能推断所有多元数据下均适用或刊本变化。
原文摘要
Rank correlations have found many innovative applications in the last decade. In particular, suitable rank correlations have been used for consistent tests of independence between pairs of random variables. Using 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 random vectors. This is the problem addressed 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 examples. In a unified study, we derive a general asymptotic representation of center-outward rank-based test statistics under independence, extending to the multivariate setting the classical Hájek asymptotic representation results. This representation permits direct calculation of limiting null distributions and facilitates a local power analysis that provides strong support for the center-outward approach by establishing, for the first time, the nontrivial power of center-outward rank-based tests over root-n neighborhoods within the class of quadratic mean differentiable alternatives.