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In this paper, we introduce a new class of models for spatial data obtainedfrom max-convolution processes based on indicator kernels with random shape. Weshow that this class of models have appealing dependence properties includingtail dependence at short distances and independence at long distances. Wefurther consider max-convolutions between such processes and processes withtail independence, in order to separately control the bulk and tail dependencebehaviors, and to increase flexibility of the model at longer distances, inparticular, to capture intermediate tail dependence. We show how parameters canbe estimated using a weighted pairwise likelihood approach, and we conduct anextensive simulation study to show that the proposed inference approach isfeasible in high dimensions and it yields accurate parameter estimates in mostcases. We apply the proposed methodology to analyse daily temperature maximameasured at 100 monitoring stations in the state of Oklahoma, US. Our resultsindicate that our proposed model provides a good fit to the data, and that itcaptures both the bulk and the tail dependence structures accurately.

Max-convolution processes with random shape indicator kernels