Open Access
November 2019 Semiparametric estimation for isotropic max-stable space-time processes
Sven Buhl, Richard A. Davis, Claudia Klüppelberg, Christina Steinkohl
Bernoulli 25(4A): 2508-2537 (November 2019). DOI: 10.3150/18-BEJ1061


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 [Buhl et al. (2018)].


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Sven Buhl. Richard A. Davis. Claudia Klüppelberg. Christina Steinkohl. "Semiparametric estimation for isotropic max-stable space-time processes." Bernoulli 25 (4A) 2508 - 2537, November 2019.


Received: 1 September 2016; Revised: 1 July 2018; Published: November 2019
First available in Project Euclid: 13 September 2019

zbMATH: 07110103
MathSciNet: MR4003556
Digital Object Identifier: 10.3150/18-BEJ1061

Keywords: Brown–Resnick process , extremogram , Max-stable process , Mixing , regular variation , Semiparametric estimation , space-time process , subsampling

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 4A • November 2019
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