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.

翻译：本文提出了一种降秩混合效应模型，用于对稀疏观测的配对函数型数据进行鲁棒建模。在该模型中，每个函数型变量的曲线通过少量函数型主成分进行概括，而两个函数型变量之间的关联则通过主成分得分的关联进行建模。采用多元尺度混合正态分布对主成分得分和测量误差进行建模，以处理异常观测值并实现鲁棒推断。均值函数和主成分函数通过样条进行建模，并施加粗糙度惩罚以避免过拟合。开发了一种期望最大化（EM）算法用于模型拟合与预测的计算。仿真研究表明，所提方法优于一种未针对鲁棒估计进行设计的现有方法。通过拟合Ia型超新星多波段光曲线的应用实例，验证了所提方法的有效性。