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Modelling pairwise dependence of maxima in space

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  • Philippe Naveau
  • Armelle Guillou
  • Daniel Cooley
  • Jean Diebolt

Abstract

We model pairwise dependence of temporal maxima, such as annual maxima of precipitation, that have been recorded in space, either on a regular grid or at irregularly spaced locations. The construction of our estimators stems from the variogram concept. The asymptotic properties of our pairwise dependence estimators are established through properties of empirical processes. The performance of our approach is illustrated by simulations and by the treatment of a real dataset. In addition to bringing new results about the asymptotic behaviour of copula estimators, the latter being linked to first-order variograms, one main advantage of our approach is to propose a simple connection between extreme value theory and geostatistics. Copyright 2009, Oxford University Press.

Suggested Citation

  • Philippe Naveau & Armelle Guillou & Daniel Cooley & Jean Diebolt, 2009. "Modelling pairwise dependence of maxima in space," Biometrika, Biometrika Trust, vol. 96(1), pages 1-17.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:1:p:1-17
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    File URL: http://hdl.handle.net/10.1093/biomet/asp001
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    Citations

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    Cited by:

    1. Papastathopoulos, Ioannis & Strokorb, Kirstin, 2016. "Conditional independence among max-stable laws," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 9-15.
    2. Whitney K. Huang & Daniel S. Cooley & Imme Ebert-Uphoff & Chen Chen & Snigdhansu Chatterjee, 2019. "New Exploratory Tools for Extremal Dependence: $$\chi $$ χ Networks and Annual Extremal Networks," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 484-501, September.
    3. Ferreira, Helena & Ferreira, Marta, 2018. "Multidimensional extremal dependence coefficients," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 1-8.
    4. Manaf Ahmed & Véronique Maume‐Deschamps & Pierre Ribereau, 2022. "Recognizing a spatial extreme dependence structure: A deep learning approach," Environmetrics, John Wiley & Sons, Ltd., vol. 33(4), June.
    5. Marcon, Giulia & Padoan, Simone & Naveau, Philippe & Muliere, Pietro & Segers, Johan, 2016. "Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials," LIDAM Discussion Papers ISBA 2016020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Keef, Caroline & Papastathopoulos, Ioannis & Tawn, Jonathan A., 2013. "Estimation of the conditional distribution of a multivariate variable given that one of its components is large: Additional constraints for the Heffernan and Tawn model," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 396-404.
    7. M. Ghil & Pascal Yiou & Stéphane Hallegatte & B. D. Malamud & P. Naveau & A. Soloviev & P. Friederichs & V. Keilis-Borok & D. Kondrashov & V. Kossobokov & O. Mestre & C. Nicolis & H. W. Rust & P. Sheb, 2011. "Extreme events: dynamics, statistics and prediction," Post-Print hal-00716514, HAL.
    8. A. Abu-Awwad & V. Maume-Deschamps & P. Ribereau, 2021. "Semiparametric estimation for space-time max-stable processes: an F-madogram-based approach," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 241-276, July.
    9. Zou, Nan, 2023. "Reweighted madogram-type estimator of Pickands dependence function," Statistics & Probability Letters, Elsevier, vol. 195(C).
    10. Boulin, Alexis & Di Bernardino, Elena & Laloë, Thomas & Toulemonde, Gwladys, 2022. "Non-parametric estimator of a multivariate madogram for missing-data and extreme value framework," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    11. Erwan Koch, 2018. "Extremal dependence and spatial risk measures for insured losses due to extreme winds," Papers 1804.05694, arXiv.org, revised Dec 2019.
    12. Bücher, Axel & Volgushev, Stanislav & Zou, Nan, 2019. "On second order conditions in the multivariate block maxima and peak over threshold method," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 604-619.
    13. A. Abu-Awwad & V. Maume-Deschamps & P. Ribereau, 2020. "Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 479-522, June.

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