Workshop: High dimensional and dependent functional data

We propose a comprehensive framework for flexible additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with spatial, temporal, or longitudinal correlation structures. Additionally, our framework includes linear effects of functional covariates and linear or smooth effects of scalar covariates that can vary smoothly over the index of the functional response and accommodates densely or sparsely observed functional responses and predictors which may be observed with additional error. Inference in this framework can be performed by standard software for generalized additive models (GAMs), allowing us to take advantage of established robust and flexible estimation algorithms. Simulation experiments show that the proposed method recovers relevant effects reliably, handles small group sizes and/or low numbers of replications well and also scales to larger data sets. Application examples on spatial and longitudinal functional data demonstrate that the proposal yields flexible model specifications that do justice to complex data situations and yield interpretable results. Jan Gertheiss, Ludwig-Maximilians-Universität München Longitudinal scalar-on-functions regression with application to tractography data Abstract: We propose a class of estimation techniques for scalar-on-function regression in longitudinal studies where both outcomes and functional predictors may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging (DTI) tractography study. One of the primary goals of the study is to