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Conditioned limit laws for inverted max-stable processes

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  • Papastathopoulos, Ioannis
  • Tawn, Jonathan A.

Abstract

Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have been proposed as an important new class for spatial extremes which are in the domain of attraction of a spatially independent max-stable process but instead they cover the broad class of asymptotic independence. To study the extreme values of such processes we use the conditioned approach to multivariate extremes that characterises the limiting distribution of appropriately normalised random vectors given that at least one of their components is large. The current statistical methods for the conditioned approach are based on a canonical parametric family of location and scale norming functions. We study broad classes of inverted max-stable processes containing processes linked to the widely studied max-stable models of Brown–Resnick and extremal-t, and identify conditions for the normalisations to either belong to the canonical family or not. Despite such differences at an asymptotic level, we show that at practical levels, the canonical model can approximate well the true conditional distributions.

Suggested Citation

  • Papastathopoulos, Ioannis & Tawn, Jonathan A., 2016. "Conditioned limit laws for inverted max-stable processes," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 214-228.
    • Handle: RePEc:eee:jmvana:v:150:y:2016:i:c:p:214-228
    DOI: 10.1016/j.jmva.2016.06.001
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    References listed on IDEAS

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    1. Opitz, T., 2013. "Extremal t processes: Elliptical domain of attraction and a spectral representation," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 409-413.
    2. Anthony W. Ledford & Jonathan A. Tawn, 1997. "Modelling Dependence within Joint Tail Regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 475-499.
    3. 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.
    4. Janet E. Heffernan & Jonathan A. Tawn, 2004. "A conditional approach for multivariate extreme values (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 497-546, August.
    5. Marc G. Genton & Yanyuan Ma & Huiyan Sang, 2011. "On the likelihood function of Gaussian max-stable processes," Biometrika, Biometrika Trust, vol. 98(2), pages 481-488.
    6. Sebastian Engelke & Alexander Malinowski & Zakhar Kabluchko & Martin Schlather, 2015. "Estimation of Hüsler–Reiss distributions and Brown–Resnick processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 239-265, January.
    7. Emma F. Eastoe & Jonathan A. Tawn, 2012. "Modelling the distribution of the cluster maxima of exceedances of subasymptotic thresholds," Biometrika, Biometrika Trust, vol. 99(1), pages 43-55.
    8. Jennifer L. Wadsworth & Jonathan A. Tawn, 2012. "Dependence modelling for spatial extremes," Biometrika, Biometrika Trust, vol. 99(2), pages 253-272.
    9. Ioannis Papastathopoulos & Jonathan A. Tawn, 2015. "Stochastic ordering under conditional modelling of extreme values: drug-induced liver injury," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(2), pages 299-317, February.
    10. R. Huser & A. C. Davison, 2013. "Composite likelihood estimation for the Brown--Resnick process," Biometrika, Biometrika Trust, vol. 100(2), pages 511-518.
    11. F. Ballani & M. Schlather, 2011. "A construction principle for multivariate extreme value distributions," Biometrika, Biometrika Trust, vol. 98(3), pages 633-645.
    12. Hilal, Sawsan & Poon, Ser-Huang & Tawn, Jonathan, 2011. "Hedging the black swan: Conditional heteroskedasticity and tail dependence in S&P500 and VIX," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2374-2387, September.
    13. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
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    Cited by:

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    2. Simpson, Emma S. & Wadsworth, Jennifer L. & Tawn, Jonathan A., 2021. "A geometric investigation into the tail dependence of vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

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