Warped Functional Regression

TL;DR

This paper introduces a functional regression method that explicitly models phase variability through time warping, improving prediction and inference for functional data with phase and amplitude variability.

Contribution

It presents a novel functional regression approach integrating time warping, enabling better handling of phase variability and unified inference.

Findings

Achieves good predictive accuracy with a parsimonious model

Derives asymptotic distribution of estimators

Demonstrates effectiveness on ozone trajectory data

Abstract

A characteristic feature of functional data is the presence of phase variability in addition to amplitude variability. Existing functional regression methods do not handle time variability in an explicit and efficient way. In this paper we introduce a functional regression method that incorporates time warping as an intrinsic part of the model. The method achieves good predictive power in a parsimonious way and allows unified statistical inference about phase and amplitude components. The asymptotic distribution of the estimators is derived and the finite-sample properties are studied by simulation. An example of application involving ground-level ozone trajectories is presented.