Inference for extremal-$t$ and skew-$t$ max-stable models in high dimensions

Abstract

Environmental phenomena are spatial processes by nature as a single extreme event (heat waves, floods, storms, etc.) often has repercussions at multiple locations. For risk management purposes it is important to have a good understanding of the dependence structure that links such events in order to make predictions on future phenomena, that can have a major impact on real life. Moreover available data at different sites can exhibit asymmetric distributions proving the necessity for max-stable processes that can handle skewness. The extremal-$t$ and skew-$t$ processes possess such flexible dependence structure between extremes and inference for these max-stable models can be performed via composite likelihood based methods. However the computational demands remains a burden in the scenario where the processes are observed at a large number of spatial locations. Assuming the time of occurrence of maxima known, the efficiency of moderately large order composite likelihood estimates is compared to those of the full likelihood approach when high dimensional information is available. Finally an illustration using maximum temperatures in the region of Melbourne, Australia, is provided.