Warped Functional Analysis of Variance

TL;DR

This paper introduces a novel functional ANOVA model that accounts for phase variability via time-warping, enabling improved analysis of functional data with amplitude and timing differences.

Contribution

It develops a unified estimation and inference framework for functional ANOVA incorporating phase variability, applicable to sparse and dense data.

Findings

Simulation studies demonstrate estimator performance.

Application to beetle growth curves illustrates practical utility.

Model handles sparse longitudinal data effectively.

Abstract

This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude and time variability. The focus is on single-random-factor models but the approach can be easily generalized to more complex ANOVA models. The behavior of the estimators is studied by simulation, and an application to the analysis of growth curves of flour beetles is presented. Although the model assumes a smooth latent process behind the observed trajectories, smoothness of the observed data is not required; the method can be applied to the sparsely observed data that is often encountered in longitudinal studies.