Modelling functional data in the presence of spatial dependence is of great practical importance as exemplified by applications in the fields of demography, economy and geography, and has received much attention recently. However, for the classical scalar-on-function regression (SoFR) with functional covariates and scalar responses, only a relatively few literature is dedicated to this relevant area, which merits further research. We propose a robust spatial autoregressive scalar-on-function regression by incorporating a spatial autoregressive parameter and a spatial weight matrix into the SoFR to accommodate spatial dependencies among individuals. The t-distribution assumption for the error terms makes our model more robust than the classical spatial autoregressive models under normal distributions. We estimate the model by firstly projecting the functional predictor onto a functional space spanned by an orthonormal functional basis and then presenting an expectation–maximization algorithm. Simulation studies show that our estimators are efficient, and are superior in the scenario with spatial correlation and heavy tailed error terms. A real weather dataset demonstrates the superiority of our model to the SoFR in the case of spatial dependence.

在空间相关的情况下对功能数据进行建模具有重要的实践意义，这在人口统计学，经济和地理领域的应用已得到充分证明，并且近来受到了广泛关注。然而，对于具有函数协变量和标量响应的经典标量函数回归（SoFR），只有相对较少的文献致力于这一相关领域，值得进一步研究。通过将空间自回归参数和空间权重矩阵合并到SoFR中，我们提出了鲁棒的空间自回归标量函数回归，以适应个体之间的空间依赖性。该Ť误差项的分布假设使我们的模型比正态分布下的经典空间自回归模型更健壮。我们首先通过将功能预测变量投影到正交功能基础所覆盖的功能空间上，然后提出期望最大化算法来估计模型。仿真研究表明，我们的估计器是有效的，并且在具有空间相关性和重尾误差项的情况下具有优越性。真实的天气数据集证明了在空间依赖性情况下我们的模型优于SoFR。