用于高维随机向量独立性的自适应正则化 CCA 检验
Adaptable Regularized CCA Tests for Independence of High-Dimensional Random Vectors
AI总结：
研究高维随机向量独立性检验，核心方法是将岭正则化和降维纳入 CCA 框架开发检验，建立渐近行为并确定参数选择方法，大量模拟研究表明该方法在多种设置下有限样本性能良好。
AI中文摘要：
我们提出了一种用于检验两个高维随机向量独立性的自适应检验方法。该方法将岭正则化和基于主成分的降维纳入典型相关分析（CCA）框架，以稳定高维环境下的经典检验统计量。根据降维情况，我们开发了正则化似然比检验和正则化最大根检验来适应不同的检验场景。我们建立了所提方法在原假设和代表性备择假设下的渐近行为，并进一步开发了一种数据驱动的方法来选择正则化参数。大量模拟研究表明在广泛的设置下具有良好的有限样本性能。
英文摘要：
We propose an adaptable testing procedure for independence between two high-dimensional random vectors. The method incorporates ridge regularization and principal component-based dimension reduction into the canonical correlation analysis (CCA) framework, thereby stabilizing classical test statistics in high-dimensional settings. Depending on the reduced dimension, we develop both a regularized likelihood ratio test and a regularized largest-root test to accommodate different testing scenarios. We establish the asymptotic behavior of the proposed procedures under both the null hypothesis and representative alternatives, and further develop a data-driven method for selecting the regularization parameter. Extensive simulation studies demonstrate favorable finite-sample performance across a broad range of settings.
