Modeling Repeated Functional Observations

We introduce a new methodological framework for repeatedly observed and thus depen-dent functional data, aiming at situations where curves are recorded repeatedly for each subject in a sample. Our methodology covers the case where the recordings of the curves are scheduled on a regular and dense grid and also situations more typical for longitudinal studies, where the timing of recordings is often sparse and random. The proposed mod-els lead to an interpretable and straightforward decomposition of the inherent variation in repeatedly observed functional data and are implemented through a straightforward two-step Functional Principal Component Analysis. We provide consistency results and asymptotic convergence rates for the estimated model components. We compare the proposed model with an alternative approach via a two-dimensional Karhunen-Loève ex-pansion and illustrate it through the analysis of longitudinal mortality data from period lifetables that are repeatedly observed for a sample of countries over many years, and also through simulation studies.