• Bernoulli
  • Volume 25, Number 4A (2019), 2508-2537.

Semiparametric estimation for isotropic max-stable space-time processes

Sven Buhl, Richard A. Davis, Claudia Klüppelberg, and Christina Steinkohl

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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)].

Article information

Bernoulli, Volume 25, Number 4A (2019), 2508-2537.

Received: September 2016
Revised: July 2018
First available in Project Euclid: 13 September 2019

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Zentralblatt MATH identifier

Brown–Resnick process extremogram max-stable process mixing regular variation semiparametric estimation space-time process subsampling


Buhl, Sven; Davis, Richard A.; Klüppelberg, Claudia; Steinkohl, Christina. Semiparametric estimation for isotropic max-stable space-time processes. Bernoulli 25 (2019), no. 4A, 2508--2537. doi:10.3150/18-BEJ1061.

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Supplemental materials

  • Supplement to “Semiparametric estimation for isotropic max-stable space-time processes”. We provide additional results on $\alpha$-mixing, subsampling for confidence regions, and a simulation study supporting the theoretical results. Our method is extended to max-stable data with observational noise and applied to both exact realizations of the Brown–Resnick process and to realizations with observational noise, thus verifying the robustness of our approach.