A0238
Title: Functional principal components from sparse functional data
Authors: Uche Mbaka - University College Dublin (Ireland) [presenting]
Jiguo Cao - Simon Fraser University (Canada)
Michelle Carey - Univerity College Dublin (Ireland)
Abstract: A novel method is introduced for extracting functional principal components from sparse functional data commonly encountered in longitudinal studies. The approach addresses the challenges posed by infrequent, irregular measurements and measurement errors. By employing conditional estimation, it effectively estimates principal scores and recovers underlying trajectories across the entire domain. A key feature is the use of a modified Gram-Schmidt orthonormalization within a reduced-rank model for the covariance function, ensuring orthogonality of eigenfunctions and positive eigenvalues. An approximate generalized cross-validation technique selects the optimal number of basis functions and principal components. Simulation studies demonstrate substantial improvements compared to existing techniques, including ReMLE, RKHS-based spectral regularization, PACE, and FACE, achieving significant gains in covariance, eigenfunction, eigenvalue, and error variance estimation, as well as curve prediction accuracy. The method is applied to analyze CD4 cell count data from the Multicenter AIDS Cohort Study. The proposed approach offers a robust and accurate tool for analyzing sparse functional data, particularly relevant in longitudinal settings.
