Modeling Spatially Dependent Functional Data by Spatial Regression with Differential Regularization

This chapter presents a semiparametric model for the analysis of functional data with spatial dependencies and space–time varying covariates. This model is based on the idea of regularized regression with a partial differential penalization term. In particular, the roughness penalty is composed by two additive terms which account for the regularity of the field in space and in time, respectively. The presented model can deal with data featuring complex dependencies induced by spatial domains featuring complex geometries. The model is applied to the analysis of the production of waste in Venice province, whose spatial domain features peninsulas and islands.