Semiparametric estimation for isotropic max-stable space-time processes

TL;DR

This paper introduces a semiparametric estimation method for extremal dependence in isotropic max-stable space-time processes, validated through simulations and applied to radar rainfall data in Florida.

Contribution

It develops a new estimation procedure based on the extremogram for modeling extremal dependence in space-time data, with proven asymptotic properties and practical confidence interval methods.

Findings

Method performs well for moderate sample sizes

Robust to small deviations from the model

Successfully applied to rainfall data in Florida

Abstract

Regularly varying space-time processes have proved useful to study extremal dependence in space-time data. We propose a semiparametric estimation procedure based on a closed form expression of the extremogram to estimate parametric models of extremal dependence functions. We establish the asymptotic properties of the resulting parameter estimates and propose subsampling procedures to obtain asymptotically correct confidence intervals. A simulation study shows that the proposed procedure works well for moderate sample sizes and is robust to small departures from the underlying model. Finally, we apply this estimation procedure to fitting a max-stable process to radar rainfall measurements in a region in Florida. Complementary results and some proofs of key results are presented together with the simulation study in the supplement.