In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the principal component functions as bivariate splines on triangulations and the principal component scores as random effects which follow an auto-regressive model. We apply the thin-plate penalty for regularizing the bivariate function estimation and develop an effective EM algorithm along with Kalman filter and smoother for calculating the penalized likelihood estimates of the parameters. Our approach was applied on simulated datasets and on Texas monthly average temperature data from January year 1915 to December year 2014.

翻译：本文提出了一种新模型，用于分析在非矩形区域上稀疏且不规则观测的、具有序列相关的二维功能数据。该方法采用混合效应模型，将主成分函数指定为三角剖分上的二元样条，并将主成分得分指定为遵循自回归模型的随机效应。我们应用薄板惩罚来正则化二元函数估计，并开发了有效的EM算法，结合卡尔曼滤波和平滑器，计算参数的惩罚似然估计。该方法在模拟数据集以及1915年1月至2014年12月德克萨斯州月平均温度数据上进行了应用。