Eigen-Adjusted Functional Principal Component Analysis
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Authors
Jiang, Ci-Ren
Lila, Eardi
Aston, John
Wang, Jane-Ling
Publication Date
2022-10-02Journal Title
Journal of Computational and Graphical Statistics
ISSN
1061-8600
Publisher
American Statistical Association
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Jiang, C., Lila, E., Aston, J., & Wang, J. (2022). Eigen-Adjusted Functional Principal Component Analysis. Journal of Computational and Graphical Statistics https://doi.org/10.1080/10618600.2022.2067550
Abstract
Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in both the mean function and the covariance function. However, methods of the first kind are not suitable for data that display second-order variation, while those of the second kind are time-consuming and make it difficult to perform subsequent statistical analyses on the dimension-reduced representations. To tackle these issues, we introduce an eigen-adjusted FPCA model that integrates covariates in the covariance function only through its eigenvalues. In particular, different structures on the covariate-specific eigenvalues -- corresponding to different practical problems -- are discussed to illustrate the model's flexibility as well as utility. To handle functional observations under different sampling schemes, we employ local linear smoothers to estimate the mean function and the pooled covariance function, and a weighted least square approach to estimate the covariate-specific eigenvalues. The convergence rates of the proposed estimators are further investigated under the different sampling schemes. In addition to simulation studies, the proposed model is applied to functional Magnetic Resonance Imaging scans, collected within the Human Connectome Project, for functional connectivity investigation.
Sponsorship
Engineering and Physical Sciences Research Council (EP/N014588/1)
EPSRC (EP/T017961/1)
Identifiers
External DOI: https://doi.org/10.1080/10618600.2022.2067550
This record's URL: https://www.repository.cam.ac.uk/handle/1810/336079
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