Multivariate Max-Stable Spatial Processes

• Activity Number: 661
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Marc G. Genton*+ and Simone Padoan and Huiyan Sang
• Companies: KAUST and Bocconi University of Milan and TAMU
• Keywords: Composite likelihood ; Cross-correlation ; Madogram ; Max-stable process ; Multivariate ; Spatial extremes

Abstract

We extend some theoretical results and applications of max-stable processes to the multivariate setting to analyze extreme events of several variables observed across space. First, we study the maxima of independent replicates of multivariate processes, both in the Gaussian and Student-t cases. We describe two important Gaussian examples and discuss possible cross-correlation models. Second, we define a Poisson process construction in the multivariate setting and introduce multivariate versions of the Smith Gaussian extreme-value, the Schlather extremal- Gaussian and extremal-t, and the Brown-Resnick models. We discuss inferential aspects for those models based on composite likelihoods, multivariate extremal coefficients and madograms. We report the results of various Monte Carlo simulations and present an application to a dataset of summer daily temperature maxima and minima in Oklahoma, USA. Joint work with Simone Padoan and Huiyan Sang.