Robust joint modeling of sparsely observed paired functional data

TL;DR

This paper introduces a robust reduced-rank mixed effects model for paired functional data that effectively handles outliers and sparsity, improving estimation accuracy through a novel EM algorithm.

Contribution

It presents a new robust modeling approach using multivariate scale mixtures and splines, specifically designed for sparse and outlier-prone paired functional data.

Findings

Outperforms existing non-robust methods in simulations

Effectively handles outliers and sparse observations

Successfully applied to supernova light curve data

Abstract

A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the association of the two functional variables is modeled through the association of the principal component scores. Multivariate scale mixture of normal distributions is used to model the principal component scores and the measurement errors in order to handle outlying observations and achieve robust inference. The mean functions and principal component functions are modeled using splines and roughness penalties are applied to avoid overfitting. An EM algorithm is developed for computation of model fitting and prediction. A simulation study shows that the proposed method outperforms an existing method which is not designed for robust estimation. The effectiveness of the proposed method is illustrated in an application of fitting multi-band light curves of Type Ia supernovae.