Functional CAR models for large spatially correlated functional datasets

Our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure, in both the space and functional domains. We show theoretically that our construction leads to a CAR model at each functional location, with spatial covariance parameters varying and borrowing strength across the functional domain.

Using basis transformation strategies, the nonseparable spatial-functional model is computationally scalable to enormous functional datasets, generalizable to different basis functions, and can be used on functions defined on higher dimensional domains such as images. Through simulation studies, we demonstrate that accounting for the spatial correlation in our modeling leads to improved functional regression performance.