An Adaptive Adjustment to the R2 Statistic in High-Dimensional Elliptical Models

• 成果类型: Article; Early Access
• 署名作者: Hong, Shizhe; Li, Weiming; Liu, Qiang; Zhang, Yangchun
• 署名单位: Shanghai University of Finance & Economics; Shanghai University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2448859
• 发表日期: 2025
• 关键词: canonical correlation-coefficients; sampling distribution; Covariance matrices; inference; eigenvalues; vectors; clt

摘要

The R-2 statistic and its classic adjusted version, say R-& lowast;2 , tend to overestimate the multiple correlation coefficient when dealing with multivariate data that exhibit heavy tails and tail dependence. This can result in an incorrect significance of correlation in high-dimensional scenarios. A new adaptive adjustment to the R-2 statistic is proposed in this article, which applies to a general population model that covers the family of elliptical distributions and an independent components model. Consistency and asymptotic normality of the new statistic are established under this general model. These findings are then applied to some fundamental inference problems in high dimensions. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.