Robust joint modelling of sparsely observed paired functional data

Abstract

A reduced-rank mixed-effects model is developed for robust modelling 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 modelled through the association of the principal component scores. A 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 modelled 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 through an application of fitting multiband light curves of Type Ia supernovae.