Max-stable processes for threshold exceedances in spatial extremes

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  • March 21, 2019
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  • Jeon, Soyoung
    • Affiliation: College of Arts and Sciences, Department of Statistics and Operations Research
Abstract
  • The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations. Multivariate extreme value theory can be used to model the joint extremal behavior of environmental data such as precipitation, snow depths or daily temperatures. Max-stable processes are the natural generalization of extremal dependence structures to infinite dimensions arising from the extension of multivariate extreme value theory. However, there have been few works on the threshold approach of max-stable processes. Padoan, Ribatet and Sisson proposed the maximum composite likelihood approach for fitting max-stable processes to avoid the complexity and unavailability of the multivariate density function. We propose the threshold version of max-stable process estimation and we apply the pairwise composite likelihood method to it. We assume a strict form of condition, so called the second-order regular variation condition, for the distribution satisfying the domain of attraction. To obtain the limit behavior, we also consider the increasing domain structure with stochastic sampling design based on the setting and conditions in Lahiri and we then establish consistency and asymptotic normality of the estimator for dependence parameter in the threshold method of max-stable processes. The method is studied by simulation and illustrated by the application of temperature data in North Carolina, United States.
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  • ... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Statistics and Operations Research.
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  • Smith, Richard L.
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