Structured Functional Principal Component Analysis

Motivated by modern observational studies, we introduce a class of functional mod-els that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where the funda-mental sampling unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for ultra-high di-mensional data. Methods are illustrated in three examples: high-frequency accelerom-eter data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep