Structured Functional Principal Component Analysis

• Activity Number: 144
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Haochang Shou*+ and Vadim Zipunnikov and Ciprian M. Crainiceanu and Sonja Greven
• Companies: Johns Hopkins Bloomberg School of Public Health and Johns Hopkins Bloomberg School of Public Health and The Johns Hopkins University and Ludwig-Maximilians-Universität München
• Keywords: functional principal component analysis ; functional linear mixed model ; variance component ; latent process

Abstract

Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where the fundamental 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 dimensional data. Methods are illustrated in three examples: high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep.