Penalized Function-on-Function Regression
A general framework for smooth regression of a functional response on one or multiple functional predictors is proposed. Using the mixed model representation of penalized regression expands the scope of function-on-function regression to many realistic scenarios. In particular, the approach can accommodate a densely or sparsely sampled functional response as well as multiple functional predictors that are observed on the same or different domains than the functional response, on a dense or sparse grid, and with or without noise. It also allows for seamless integration of continuous or categorical covariates and provides approximate confidence intervals as a by-product of the mixed model inference. The proposed methods are accompanied by easy to use and robust software implemented in the pffr function of the R package refund. Methodological developments are general, but were inspired by and applied to a diffusion tensor imaging brain tractography dataset.
MSU Digital Commons Citation
Ivanescu, Andrada; Staicu, Ana Maria; Scheipl, Fabian; and Greven, Sonja, "Penalized Function-on-Function Regression" (2015). Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works. 102.