Dynamic Retrospective Regression for Functional Data

TL;DR

This paper introduces a novel functional regression method that effectively incorporates phase synchronization, improving prediction accuracy for functional data with phase variability, demonstrated through simulations and neuromotor data analysis.

Contribution

It proposes a new regression approach that integrates phase synchronization directly into the model, addressing a key limitation of existing methods.

Findings

Enhanced predictive power over traditional linear regression

Effective handling of phase variability in functional data

Validated through simulation and neuromotor data analysis

Abstract

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.