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Modeling the Extremes of Bivariate Mixture Distributions With Application to Oceanographic Data

Author

Listed:
  • Stan Tendijck
  • Emma Eastoe
  • Jonathan Tawn
  • David Randell
  • Philip Jonathan

Abstract

There currently exist a variety of statistical methods for modeling bivariate extremes. However, when the dependence between variables is driven by more than one latent process, these methods are likely to fail to give reliable inferences. We consider situations in which the observed dependence at extreme levels is a mixture of a possibly unknown number of much simpler bivariate distributions. For such structures, we demonstrate the limitations of existing methods and propose two new methods: an extension of the Heffernan–Tawn conditional extreme value model to allow for mixtures and an extremal quantile-regression approach. The two methods are examined in a simulation study and then applied to oceanographic data. Finally, we discuss extensions including a subasymptotic version of the proposed model, which has the potential to give more efficient results by incorporating data that are less extreme. Both new methods outperform existing approaches when mixtures are present.

Suggested Citation

  • Stan Tendijck & Emma Eastoe & Jonathan Tawn & David Randell & Philip Jonathan, 2023. "Modeling the Extremes of Bivariate Mixture Distributions With Application to Oceanographic Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1373-1384, April.
  • Handle: RePEc:taf:jnlasa:v:118:y:2023:i:542:p:1373-1384
    DOI: 10.1080/01621459.2021.1996379
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