Eigen-Adjusted Functional Principal Component Analysis

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 both and covariance function. However, methods of first kind not suitable that display second-order variation, while those second time-consuming make it difficult to perform subsequent statistical analyses on dimension-reduced representations. To tackle these issues, we introduce an eigen-adjusted model integrates only through its eigenvalues. In particular, different structures covariate-specific eigenvalues—corresponding practical problems—are discussed illustrate model’s flexibility as well utility. handle observations under sampling schemes, employ local linear smoothers estimate pooled function, weighted least square approach The convergence rates proposed estimators further investigated schemes. addition simulation studies, is applied Magnetic Resonance Imaging scans, collected within Human Connectome Project, connectivity investigation. Supplementary materials this article available online.