Exploring Nonlinear Spatial Dependence in the Tails

In many instances it is of interest to measure the degree of similarity between neighboring regions. Spatial autocorrelation measures are the most popular means of doing it. However, such measures only capture a global linear relationship between regions, whereas in many circumstances a more general instrument is required. For instance, in economic poverty analysis or environmental applications (and in other cases where we are interested in extreme events and threshold exceedances) we should be more interested in the spatial pattern in the tails of the joint distributions. In this article we introduce some exploratory tool that focuses on the bivariate joint tails behavior to detect a pattern of spatial regularities. The method will be illustrated with reference to simulated environmental data.