Higher-Order Spatial Structure Functions for Exploring Spatial Extremes
Date:
Spatial statistics has long relied on measures of second-order dependence (e.g., covariance functions and variograms) to characterize and model spatial dependence. In the turbulence literature, higher-order spatial dependence measures, such as third and fourth-order structure functions (variograms) have been instrumental in characterizing important behavior such as turbulent energy cascades. Here, we investigate the use of these higher-order structure functions to better characterize the dependence structure of spatial extremes, which can help with the specification of appropriate statistical models for such dependence. We illustrate the approach on simulated and real-world environmental data.