稀疏观测配对函数型数据的稳健联合建模
Robust joint modeling of sparsely observed paired functional data
AI总结：
本文提出一种基于降秩混合效应模型和多元正态尺度混合分布的稳健联合建模方法，用于稀疏观测配对函数型数据，并通过EM算法实现拟合，在超新星光变曲线应用中验证了其优于现有方法的效果。
摘要：
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稳健建模。在该模型中，每个函数型变量的曲线通过若干函数型主成分进行概括，两个函数型变量之间的关联则通过主成分得分之间的关联来建模。采用多元正态尺度混合分布对主成分得分和测量误差进行建模，以处理异常观测并实现稳健推断。均值函数和主成分函数使用样条进行建模，并施加粗糙度惩罚以避免过拟合。开发了一种EM算法用于模型拟合与预测的计算。模拟研究表明，所提出的方法优于一种未针对稳健估计设计的现有方法。该方法在拟合Ia型超新星多波段光变曲线的应用中展示了其有效性。
英文摘要：
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.
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