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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

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  • Keef, Caroline
  • Papastathopoulos, Ioannis
  • Tawn, Jonathan A.

Abstract

A number of different approaches to study multivariate extremes have been developed. Arguably the most useful and flexible is the theory for the distribution of a vector variable given that one of its components is large. We build on the conditional approach of Heffernan and Tawn (2004) [13] for estimating this type of multivariate extreme property. Specifically we propose additional constraints for, and slight changes in, their model formulation. These changes in the method are aimed at overcoming complications that have been experienced with using the approach in terms of their modelling of negatively associated variables, parameter identifiability problems and drawing conditional inferences which are inconsistent with the marginal distributions. The benefits of the methods are illustrated using river flow data from two tributaries of the River Thames in the UK.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:396-404
    DOI: 10.1016/j.jmva.2012.10.012
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    References listed on IDEAS

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    1. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
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    7. Frick, Melanie & Reiss, Rolf-Dieter, 2009. "Expansions of multivariate Pickands densities and testing the tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1168-1181, July.
    8. Einmahl, J.H.J. & de Haan, L.F.M. & Piterbarg, V.I., 2001. "Nonparametric estimation of the spectral measure of an extreme value distribution," Other publications TiSEM c3485b9b-a0bd-456f-9baa-0, Tilburg University, School of Economics and Management.
    9. Caroline Keef & Jonathan Tawn & Cecilia Svensson, 2009. "Spatial risk assessment for extreme river flows," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(5), pages 601-618, December.
    10. 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.
    11. Alexandra Ramos & Anthony Ledford, 2009. "A new class of models for bivariate joint tails," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 219-241, January.
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    Cited by:

    1. Marmai, Nadin & Franco Villoria, Maria & Guerzoni, Marco, 2016. "How the Black Swan damages the harvest: statistical modelling of extreme events in weather and crop production in Africa, Asia, and Latin America," Department of Economics and Statistics Cognetti de Martiis LEI & BRICK - Laboratory of Economics of Innovation "Franco Momigliano", Bureau of Research in Innovation, Complexity and Knowledge, Collegio 201605, University of Turin.
    2. Liu, Y. & Tawn, J.A., 2014. "Self-consistent estimation of conditional multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 19-35.
    3. Li, Xuan & Zhang, Wei, 2020. "Long-term assessment of a floating offshore wind turbine under environmental conditions with multivariate dependence structures," Renewable Energy, Elsevier, vol. 147(P1), pages 764-775.
    4. de Valk, Cees, 2016. "A large deviations approach to the statistics of extreme events," Other publications TiSEM 117b3ba0-0e40-4277-b25e-d, Tilburg University, School of Economics and Management.
    5. 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.
    6. Daniel Maposa & Anna M. Seimela & Caston Sigauke & James J. Cochran, 2021. "Modelling temperature extremes in the Limpopo province: bivariate time-varying threshold excess approach," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(3), pages 2227-2246, July.
    7. Stan Tendijck & Philip Jonathan & David Randell & Jonathan Tawn, 2024. "Temporal evolution of the extreme excursions of multivariate k$$ k $$th order Markov processes with application to oceanographic data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    8. Marmai, Nadine, 2016. "Farmers’ investments in innovative technologies in times of precipitation extremes: A statistical analysis for rural Tanzania," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201617, University of Turin.
    9. Caston Sigauke & Thakhani Ravele & Lordwell Jhamba, 2022. "Extremal Dependence Modelling of Global Horizontal Irradiance with Temperature and Humidity: An Application Using South African Data," Energies, MDPI, vol. 15(16), pages 1-25, August.
    10. Richards, Jordan & Tawn, Jonathan A., 2022. "On the tail behaviour of aggregated random variables," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    11. 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.
    12. Klaus Schneeberger & Matthias Huttenlau & Benjamin Winter & Thomas Steinberger & Stefan Achleitner & Johann Stötter, 2019. "A Probabilistic Framework for Risk Analysis of Widespread Flood Events: A Proof‐of‐Concept Study," Risk Analysis, John Wiley & Sons, vol. 39(1), pages 125-139, January.
    13. Hugo C. Winter & Jonathan A. Tawn, 2016. "Modelling heatwaves in central France: a case-study in extremal dependence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(3), pages 345-365, April.
    14. R. Shooter & E. Ross & A. Ribal & I. R. Young & P. Jonathan, 2021. "Spatial dependence of extreme seas in the North East Atlantic from satellite altimeter measurements," Environmetrics, John Wiley & Sons, Ltd., vol. 32(4), June.
    15. C. J. R. Murphy‐Barltrop & J. L. Wadsworth & E. F. Eastoe, 2023. "New estimation methods for extremal bivariate return curves," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.

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