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AbstractSpatial extreme value analysis is useful to environmental studies, in which extreme value phenomena are of interest and meaningful spatial patterns can be discerned. Max-stable process models are able to describe such phenomena. This class of models is asymptotically justified to characterize the spatial dependence among extremes. However, likelihood inference is challenging for such models because their corresponding joint likelihood is unavailable and only bivariate or trivariate distributions are known. In this paper, we propose a tapered composite likelihood approach by utilizing lower dimensional marginal likelihoods for inference on parameters of various max-stable process models. We consider a weighting strategy based on a "taper range" to exclude distant pairs or triples. The "optimal taper range" is selected to maximize various measures of the Godambe information associated with the tapered composite likelihood function. This method substantially reduces the computational cost and improves the efficiency over equally weighted composite likelihood estimators. We illustrate its utility with simulation experiments and an analysis of rainfall data in Switzerland.
SponsorsThe research of Huiyan Sang was partially supported by NSF grant DMS-1007618. Marc G. Genton's work was partially supported by DMS-1007504 and DMS-1100492. Both authors were supported by Award Number KUS-CI-016-04, from King Abdullah University of Science and Technology (KAUST). The authors thank Dr. Anthony Davison and Dr. Mathieu Ribatet for several useful discussions regarding this work and for providing the Swiss precipitation dataset.