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.

中文翻译：

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稀疏观测的配对函数数据的鲁棒联合建模

开发了降秩混合效应模型，用于对稀疏观察的配对功能数据进行鲁棒建模。在此模型中，使用几个功能主成分总结每个功能变量的曲线，并通过主成分分数的关联对两个功能变量的关联进行建模。使用正态分布的多变量尺度混合来对主成分分数和测量误差进行建模，以处理异常观测值并实现稳健的推理。使用样条函数对均值函数和主成分函数进行建模，并应用粗糙度惩罚来避免过度拟合。开发了 EM 算法来计算模型拟合和预测。仿真研究表明，所提出的方法优于现有方法，这不是为稳健估计而设计的。通过对 Ia 型超新星多波段光变曲线的拟合应用说明了该方法的有效性。