A robust spatial autoregressive scalar-on-function regression with t-distribution

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.