title: Structured functional principal component analysis.
abstract: Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental 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 high-dimensional data. Methods are used in applications including high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep.
authors.affiliation: Department of Biostatistics and Epidemiology, University of Pennsylvania, Perelman School of Medicine, Philadelphia, Pennsylvania, U.S.A.
authors.forename: Haochang
authors.initials: H
authors.lastname: Shou
authors.affiliation: Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, U.S.A.
authors.forename: Vadim
authors.initials: V
authors.lastname: Zipunnikov
authors.affiliation: Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, U.S.A.
authors.forename: Ciprian M
authors.initials: CM
authors.lastname: Crainiceanu
authors.affiliation: Department of Statistics, Ludwig-Maximilians-Universität München, Munich, Germany.
authors.forename: Sonja
authors.initials: S
authors.lastname: Greven
mesh_terms: D000465:Algorithms; D003627:Data Interpretation, Statistical; D003936:Diagnosis, Computer-Assisted / Q000379:methods*; D006801:Humans; D008991:Monitoring, Physiologic / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D025341:Principal Component Analysis; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Functional linear mixed model; Functional principal component analysis; Latent process; Multilevel correlation structure; Variance component