Threshold Approach in the Analysis of Spatial Extremes

• Activity Number: 329
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Soyoung Jeon*+
• Companies: The University of North Carolina at Chapel Hill
• Keywords: spatial extremes ; max-stable process ; threshold approach ; composite likelihood

Abstract

The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations. Max-stable processes, a natural generalization of multivariate extreme value theory, can be used to model the joint extremal behavior of environmental data such as precipitation, snow depth or temperature. However, there have been few works on the threshold approach of max-stable processes. Padoan, Ribatet and Sisson [2010] 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. Based on the increasing domain structure with stochastic sampling design in Lahiri [2003], we then establish consistency and asymptotic normality of the estimator for dependence parameter. The method is studied by simulation and illustrated by the application of temperature data in North Carolina, United States.