Dynamic Retrospective Regression for Functional Data

Samples of curves, or functional data, usually present phase variability in addition to amplitude variability. Existing functional regression methods do not handle phase variability in an efficient way. In this paper we propose a functional regression method that incorporates phase synchronization as an intrinsic part of the model, and then attains better predictive power than ordinary linear regression in a simple and parsimonious way. The finite-sample properties of the estimators are studied by simulation. As an example of application, we analyze neuromotor data arising from a study of human lip movement.