IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v155y2017icp52-71.html
   My bibliography  Save this article

Properties of extremal dependence models built on bivariate max-linearity

Author

Listed:
  • Kereszturi, Mónika
  • Tawn, Jonathan

Abstract

Bivariate max-linear models provide a core building block for characterizing bivariate max-stable distributions. The limiting distribution of marginally normalized component-wise maxima of bivariate max-linear models can be dependent (asymptotically dependent) or independent (asymptotically independent). However, for modeling bivariate extremes they have weaknesses in that they are exactly max-stable with no penultimate form of convergence to asymptotic dependence, and asymptotic independence arises if and only if the bivariate max-linear model is independent. In this work we present more realistic structures for describing bivariate extremes. We show that these models are built on bivariate max-linearity but are much more general. In particular, we present models that are dependent but asymptotically independent and others that are asymptotically dependent but have penultimate forms. We characterize the limiting behavior of these models using two new different angular measures in a radial–angular representation that reveal more structure than existing measures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:52-71
    DOI: 10.1016/j.jmva.2016.12.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16302159
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.12.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Jennifer L. Wadsworth & Jonathan A. Tawn, 2012. "Dependence modelling for spatial extremes," Biometrika, Biometrika Trust, vol. 99(2), pages 253-272.
    5. 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.
    6. Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Richards, Jordan & Tawn, Jonathan A., 2022. "On the tail behaviour of aggregated random variables," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    2. 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.
    3. 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.
    4. Lee Fawcett & David Walshaw, 2014. "Estimating the probability of simultaneous rainfall extremes within a region: a spatial approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(5), pages 959-976, May.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
    9. 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.
    10. Murphy-Barltrop, C.J.R. & Wadsworth, J.L., 2024. "Modelling non-stationarity in asymptotically independent extremes," Computational Statistics & Data Analysis, Elsevier, vol. 199(C).
    11. 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.
    12. 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.
    13. 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.
    14. Jordan Richards & Jennifer L. Wadsworth, 2021. "Spatial deformation for nonstationary extremal dependence," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.
    15. 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.
    16. 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.
    17. 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.
    18. Marta Ferreira & Helena Ferreira, 2017. "Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective," Risks, MDPI, vol. 5(3), pages 1-12, June.
    19. Refk Selmi & Christos Kollias & Stephanos Papadamou & Rangan Gupta, 2017. "A Copula-Based Quantile-on-Quantile Regression Approach to Modeling Dependence Structure between Stock and Bond Returns: Evidence from Historical Data of India, South Africa, UK and US," Working Papers 201747, University of Pretoria, Department of Economics.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:52-71. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.