Testing Independence and Conditional Independence in High Dimensions via Coordinatewise Gaussianization

• 成果类型: Article; Early Access
• 署名作者: Chang, Jinyuan; Du, Yue; He, Jing; Yao, Qiwei
• 署名单位: Southwestern University of Finance & Economics - China; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Peking University; Southwestern University of Finance & Economics - China; University of London; London School Economics & Political Science
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2637891
• 发表日期: 2026-05-27
• 关键词: Conditional independence test; Coordinatewise Gaussianization; Gaussian Approximation; High-dimensional statistical inference; Independence test; multiplier bootstrap; distance correlation; nonparametric test; covariance; dependence; association; bootstrap; sums; sets

摘要

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, that is, we first transform each component variable to the standard normal via its marginal empirical distribution, and we then test for independence and conditional independence of the transformed random vectors using appropriate L infinity-type test statistics. While we are testing some necessary conditions of the independence or the conditional independence, the new tests outperform the 13 frequently used testing methods in a large scale simulation comparison. The advantage of the new tests can be summarized as follows: (i) they do not require any moment conditions, (ii) they allow arbitrary dependence structures of the components among the random vectors, and (iii) they allow the dimensions of random vectors to diverge at the exponential rates of the sample size. The critical values of the proposed tests are determined by a computationally efficient multiplier bootstrap procedure. Theoretical analysis shows that the sizes of the proposed tests can be well controlled by the nominal significance level, and the proposed tests are also consistent under certain local alternatives. The finite sample performance of the new tests is illustrated via extensive simulation studies and a real data application. Supplementary materials for this article are available online.