A test of weak separability for multi-way functional data, with application to brain connectivity studies

• 成果类型: Article
• 署名作者: Lynch, Brian; Chen, Kehui
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy048
• 发表日期: 2018
• 页码: 815831
• 关键词: human connectome project; COVARIANCE-MATRIX; dimension; Operators; SPACE

摘要

This paper concerns the modelling of multi-way functional data where double or multiple indices are involved. We introduce a concept of weak separability. The weakly separable structure supports the use of factorization methods that decompose the signal into its spatial and temporal components. The analysis reveals interesting connections to the usual strongly separable covariance structure, and provides insights into tensor methods for multi-way functional data. We propose a formal test for the weak separability hypothesis, where the asymptotic null distribution of the test statistic is a chi-squared-type mixture. The method is applied to study brain functional connectivity derived from source localized magnetoencephalography signals during motor tasks.