Longitudinal Functional Data Analysis
Ana-Maria Staicu, North Carolina State University
We consider functional data that are correlated because of a longitudinal-based design: each subject is observed at repeated time visits and for each visit we record a functional variable. In this setting we discuss two important problems: statistical inference for fixed effects and parsimonious modeling framework. For the first problem we consider bootstrap of independent units (subjects) to quantify the variability of the fixed effects and develop testing procedures that formally assess whether the mean response varies over visits. For the second problem we propose an approach that accurately describes the process dynamics over visits and provides prediction of a full trajectory at a future visit. The proposed methodologies are investigated numerically in finite samples. The methods are applied to the Baltimore Longitudinal Study of Aging (BLSA) and a longitudinal diffusion tensor imaging study of multiple sclerosis.