Generalized ridge penalization for trend modeling and spatial prediction with generalized additive models

Abstract In this study, we explore the utility of Generalized Ridge Generalized Additive Models (GAMs) for trend modeling and spatial prediction. Trend modeling is conducted through an iterative procedure that updates the covariance matrix of the residuals at each step. This matrix is also estimated using a simple GAM-based approach that relates the residuals at different locations through a model with a coefficient depending on the distance between each pair of points. Spatial prediction is achieved by adding to the trend model new terms whose coefficients depend on the distance of each target point to its k nearest neighbors. The performance of the proposed methodology is assessed using synthetic data. Furthermore, a case study is presented involving the estimation of the underlying spatial distribution of a heavy metal from a public dataset. In both scenarios – synthetic and real-world – a comparative analysis for spatial prediction with universal kriging is performed.