Testing General Linear Hypotheses Under a High-Dimensional Multivariate Regression Model with Spiked Noise Covariance

• 成果类型: Article
• 署名作者: Li, Haoran; Aue, Alexander; Paul, Debashis; Peng, Jie
• 署名单位: Auburn University System; Auburn University; University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2278825
• 发表日期: 2024
• 页码: 2799-2810
• 关键词: Principal component analysis; fmri; eigenvalues; asymptotics; number

摘要

We consider the problem of testing linear hypotheses under a multivariate regression model with a high-dimensional response and spiked noise covariance. The proposed family of tests consists of test statistics based on a weighted sum of projections of the data onto the estimated latent factor directions, with the weights acting as the regularization parameters. We establish asymptotic normality of the test statistics under the null hypothesis. We also establish the power characteristics of the tests and propose a data-driven choice of the regularization parameters under a family of local alternatives. The performance of the proposed tests is evaluated through a simulation study. Finally, the proposed tests are applied to the Human Connectome Project data to test for the presence of associations between volumetric measurements of human brain and behavioral variables. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.