An Adaptive Adjustment to the R 2 Statistic in High-Dimensional Elliptical Models
针对厚尾和尾部依赖的多变量数据，提出一种新的R²统计量自适应调整方法，适用于椭圆分布和独立成分模型，并建立了相合性和渐近正态性，解决高维场景下相关性的错误显著性判断问题。
The 𝑅2 statistic and its classic adjusted version, say 𝑅*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 𝑅2 statistic is proposed in this paper, 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.