Abstract: Rank-based measures are widely used to assess statistical dependence among variables. In this paper, we propose a family of multi-level thresholding tests for high-dimensional independence based on five rank-based dependence measures: Kendall's tau, Spearman's rho, Hoeffding's D, Blum–Kiefer–Rosenblatt's R, and Bergsma–Dassios–Yanagimoto's tau*. By adaptively selecting the threshold level, the proposed tests accommodate alternatives with varying degrees of signal sparsity. We derive their detection boundaries under sparse alternatives, characterizing the relationship between signal sparsity and the strength required for detection. Our theoretical results identify regimes in which the proposed tests can detect sparse and weak dependence signals that may escape conventional rank-based sum- and max-type tests. Simulation studies support the theoretical findings and evaluate the finite-sample performance of the proposed tests.

 

个人简介：周叶青，同济大学数学科学学院长聘教授，博士生导师。入选国家高层次人才计划青年项目，小米青年学者。研究方向为复杂数据关联分析与统计推断等。作为项目负责人，主持国家重点研发计划青年科学家项目，国家自然科学基金面上与青年、上海市自然科学基金面上等项目。