An Overview of Kriging and Cokriging Predictors for Functional Random Fields

This article presents an overview of methodologies for spatial prediction of functional data, focusing on both stationary and non-stationary conditions. A significant aspect of the functional random fields analysis is evaluating stationarity to characterize the stability of statistical properties across the spatial domain. The article explores methodologies from the literature, providing insights into the challenges and advancements in functional geostatistics. This work is relevant from theoretical and practical perspectives, offering an integrated view of methodologies tailored to the specific stationarity conditions of the functional processes under study. The practical implications of our work span across fields like environmental monitoring, geosciences, and biomedical research. This overview encourages advancements in functional geostatistics, paving the way for the development of innovative techniques for analyzing and predicting spatially correlated functional data. It lays the groundwork for future research, enhancing our understanding of spatial statistics and its applications.

Automated summary

This article provides an overview of spatial prediction methodologies for functional data, covering both stationary and non-stationary conditions. The evaluation of stationarity is an important aspect in functional random fields analysis to assess the stability of statistical properties across spatial areas. The article examines existing methodologies from the literature and offers insights into the challenges and progress in functional geostatistics. This work is significant from both theoretical and practical perspectives, offering an integrated approach tailored to the specific stationarity conditions of the functional processes under investigation.