Depth-based estimation for multivariate functional data with phase variability

TL;DR

This paper introduces a robust depth-based method for estimating the central pattern in multivariate functional data with phase variability and cross-component time warping, addressing challenges of time distortion and outliers.

Contribution

It develops a new approach that leverages depth functions to consistently estimate the main pattern in complex multivariate functional data with phase variability and warping.

Findings

Method performs well in simulations under various model assumptions.

The approach is robust against atypical observations and model violations.

Application to real data demonstrates practical utility.

Abstract

In the context of multivariate functional data with individual phase variation, we develop a robust depth-based approach to estimate the main pattern function when cross-component time warping is also present. In particular, we consider the latent deformation model (Carroll and M\"uller, 2023) in which the different components of a multivariate functional variable are also time-distorted versions of a common template function. Rather than focusing on a particular functional depth measure, we discuss the necessary conditions on a depth function to be able to provide a consistent estimation of the central pattern, considering different model assumptions. We evaluate the method performance and its robustness against atypical observations and violations of the model assumptions through simulations, and illustrate its use on two real data sets.