Applied Mathematics Commons^™

Penalized Function-On-Function Regression, Andrada Ivanescu, Ana Maria Staicu, Fabian Scheipl, Sonja Greven

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

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 …