Functional Data Analysis for Sparse Longitudinal Data

We propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data. The method aims at irregularly spaced longitudinal data, where the number of repeated measurements available per subject is small. In contrast, classical functional data analysis requires a large number of regularly spaced measurements per subject. We assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random (subject-specific) trajectory plus measurement errors. Basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the…