  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.
