Estimating Spatial Anisotropy in Semiparametric Regression with Differential Regularization

Spatial regression models play a crucial role in analyzing environmental data and predicting spatially distributed phenomena. However, traditional approaches often struggle to capture the complex spatial dependencies and non-stationarities present in real-world datasets. In this paper, we propose a novel parameter cascading algorithm for spatial regression. The algorithm allows for the simultaneous estimation of the unknown spatial parameters describing the anisotropy and the spatial field itself, while incorporating physical and domain knowledge. We illustrate the proposed algorithm through an application to the analysis of rainfall data in Switzerland. The parameter cascading algorithm enables more accurate and localized predictions of spatially distributed variables.