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Dense classes of multivariate extreme value distributions

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  • Fougères, Anne-Laure
  • Mercadier, Cécile
  • Nolan, John P.

Abstract

In this paper, we explore tail dependence modeling in multivariate extreme value distributions. The measure of dependence chosen is the scale function, which allows combinations of distributions in a very flexible way. The correspondences between the scale function and the spectral measure or the stable tail dependence function are given. Combining scale functions by simple operations, three parametric classes of laws are (re)constructed and analyzed, and resulting nested and structured models are discussed. Finally, the denseness of each of these classes is shown.

Suggested Citation

  • Fougères, Anne-Laure & Mercadier, Cécile & Nolan, John P., 2013. "Dense classes of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 109-129.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:109-129
    DOI: 10.1016/j.jmva.2012.11.015
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    1. Einmahl, J.H.J. & Krajina, A. & Segers, J.J.J., 2007. "A Method of Moments Estimator of Tail Dependence," Other publications TiSEM 6ee60ab8-3c01-4bd9-aa5e-7, Tilburg University, School of Economics and Management.
    2. Einmahl, J.H.J. & Krajina, A. & Segers, J., 2011. "An M-Estimator for Tail Dependence in Arbitrary Dimensions," Discussion Paper 2011-013, Tilburg University, Center for Economic Research.
    3. Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
    4. Anne‐Laure Fougères & John P. Nolan & Holger Rootzén, 2009. "Models for Dependent Extremes Using Stable Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 42-59, March.
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    Cited by:

    1. Charpentier, A. & Fougères, A.-L. & Genest, C. & Nešlehová, J.G., 2014. "Multivariate Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 118-136.
    2. Kereszturi, Mónika & Tawn, Jonathan, 2017. "Properties of extremal dependence models built on bivariate max-linearity," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 52-71.
    3. Miranda J. Fix & Daniel S. Cooley & Emeric Thibaud, 2021. "Simultaneous autoregressive models for spatial extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    4. Samuel A. Morris & Brian J. Reich & Emeric Thibaud, 2019. "Exploration and Inference in Spatial Extremes Using Empirical Basis Functions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 555-572, December.
    5. Klüppelberg, Claudia & Krali, Mario, 2021. "Estimating an extreme Bayesian network via scalings," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    6. Enkelejd Hashorva & Simone A. Padoan & Stefano Rizzelli, 2021. "Multivariate extremes over a random number of observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 845-880, September.
    7. Durieu, Olivier & Wang, Yizao, 2022. "Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 55-88.

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