A Non-parametric Approach Based on RDDs to the Estimation of Non-stationary Spatial Covariance Functions

Estimating non-stationary spatial processes is a key challenge in geostatistics, particularly for Earth sciences applications. Based on our recent work [10], this communication describes a novel estimation method based on Random Domain Decomposition (RDD), which circumvents the limitations of fixed-grid methods by leveraging random partitions of the spatial domain. Building on the non-stationary Matern covariance model, RDD assumes local stationarity within subdomains, estimates parameters using standard variogram techniques, and aggregates results across multiple partitions to provide robust and flexible estimates of the target covariance kernel. Through extensive simulations and application to real-world data, RDD demonstrates superior efficiency and accuracy over conventional approaches, providing a scalable and interpretable solution for modeling spatial non-stationarity.