A0651
Title: Eigen-adjusted functional principal component analysis
Authors: Ci-Ren Jiang - National Taiwan University (Taiwan) [presenting]
Eardi Lila - University of Washington (United States)
Jane-Ling Wang - University of California Davis (United States)
John Aston - University of Cambridge (United Kingdom)
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 unsuitable 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, an eigen-adjusted FPCA model is introduced 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 and utility. To handle functional observations under different sampling schemes, local linear smoother to estimate the mean function and the pooled covariance function and a weighted least square approach to estimate the covariate-specific eigenvalues are employed. 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.
