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Non-Stationary Dependence Structures for Spatial Extremes

Author

Listed:
  • Raphaël Huser

    (King Abdullah University of Science and Technology)

  • Marc G. Genton

    (King Abdullah University of Science and Technology)

Abstract

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. In this paper, we develop non-stationary max-stable dependence structures in which covariates can be easily incorporated. Inference is performed using pairwise likelihoods, and its performance is assessed by an extensive simulation study based on a non-stationary locally isotropic extremal t model. Evidence that unknown parameters are well estimated is provided, and estimation of spatial return level curves is discussed. The methodology is demonstrated with temperature maxima recorded over a complex topography. Models are shown to satisfactorily capture extremal dependence.

Suggested Citation

  • Raphaël Huser & Marc G. Genton, 2016. "Non-Stationary Dependence Structures for Spatial Extremes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 470-491, September.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:3:d:10.1007_s13253-016-0247-4
    DOI: 10.1007/s13253-016-0247-4
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    2. J. Mateu & E. Porcu, 2016. "Guest Editors’ Introduction to the Special Issue on “Seismomatics: Space–Time Analysis of Natural or Anthropogenic Catastrophes”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 403-406, September.
    3. Krupskii, Pavel & Huser, Raphaël, 2024. "Max-convolution processes with random shape indicator kernels," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    4. Kiriliouk, Anna, 2017. "Hypothesis testing for tail dependence parameters on the boundary of the parameter space with application to generalized max-linear models," LIDAM Discussion Papers ISBA 2017027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.
    6. Daniela Castro Camilo & Miguel de Carvalho & Jennifer Wadsworth, 2017. "Time-Varying Extreme Value Dependence with Application to Leading European Stock Markets," Papers 1709.01198, arXiv.org.

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