A flexible special case of the CSN for spatial modeling and prediction

We introduce a parsimonious, flexible subclass of the closed-skew normal (CSN) distribution that produces valid stationary spatial models. We derive and prove some relevant properties for this subfamily; in particular, we show that it is identifiable, closed under marginalization and conditioning and that a null correlation implies independence. Based on the subclass, we propose a discrete spatial model and its continuous version. We discuss why these random fields constitute valid models, and additionally, we discuss least-squares estimators for the models under the subclass. We propose to perform predictions on the model using the profile predictive likelihood; we discuss how to construct prediction regions and intervals. To compare the model against its Gaussian counterpart and show that the numerical likelihood estimators are well-behaved, we present a simulation study. Finally, we use the model to study a heuristic COVID-19 mortality risk index; we evaluate the model's performance through 10-fold cross-validation. The risk index model is compared with a baseline Gaussian model.