Distribution-free tests of independence in high dimensions

• 成果类型: Article
• 署名作者: Han, Fang; Chen, Shizhe; Liu, Han
• 署名单位: University of Washington; University of Washington Seattle; Columbia University; Princeton University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx050
• 发表日期: 2017
• 页码: 813828
• 关键词: linear rank statistics; sample correlation-matrices; likelihood ratio tests; COVARIANCE-MATRIX; large deviations; asymptotic distributions; largest entries; LIMIT-THEOREMS; coherence; UNIVERSALITY

摘要

We consider the testing of mutual independence among all entries in a d-dimensional random vector based on n independent observations. We study two families of distribution-free test statistics, which include Kendall's tau and Spearman's rho as important examples. We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and we propose tests that control the Type I error in the high-dimensional setting where d > n. We further show that the two tests are rate-optimal in terms of power against sparse alternatives and that they outperform competitors in simulations, especially when d is large.