M-Estimation for Max-Stable Random Fields via CRPS

• Activity Number: 241
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Robert Yuen*+ and Stilian A Stoev
• Companies: University of Michigan Department of Statistics and University of Michigan
• Keywords: spatial ; extremes ; max-stable ; rainfall ; M-estimation ; CRPS

Abstract

Max-stable random fields provide canonical models for spatial extremes. Inference in such models has been challenging due to the lack of tractable likelihoods. In contrast, the finite dimensional cumulative distribution functions (CDFs) are often readily available and natural to work with. Motivated by this fact, we develop an M-estimation framework for max-stable models based on the continuous ranked probability score (CRPS) of multivariate CDFs. We establish conditions for the consistency and asymptotic normality of the CRPS based estimators in a general context. We then implement them in the max-stable setting and provide readily computable expressions for their asymptotic covariance matrices. The resulting point and asymptotic condence interval estimates are illustrated over popular simulated models. The new CRPS-based estimators were used to study rainfall extremes in Switzerland.