Spectral density regression for bivariate extremes

Abstract

We introduce a density regression model for the spectral density of a bivariate extreme value distribution, that allows us to assess how extremal dependence can change over a covariate. Inference is performed through a double kernel estimator, which can be seen as an extension of the Nadaraya–Watson estimator where the usual scalar responses are replaced by mean constrained densities on the unit interval. Numerical experiments with the methods illustrate their resilience in a variety of contexts of practical interest. An extreme temperature dataset is used to illustrate our methods.

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Acknowledgments

We thank the editor, associate editor, and reviewers for helpful comments and suggestions on an earlier draft of this article. We extend our thanks to Vanda Inácio de Carvalho, Rodrigo Herrera, Raphael Huser, and Jenny Wadsworth for discussions, and to Edgardo Dörner for computational support. This research was partially supported by the Fondecyt project 11121186.

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Correspondence to Miguel de Carvalho.

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Castro Camilo, D., de Carvalho, M. Spectral density regression for bivariate extremes. Stoch Environ Res Risk Assess 31, 1603–1613 (2017). https://doi.org/10.1007/s00477-016-1257-z

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Keywords

  • Bivariate extremes values
  • Nonstationary extremal dependence structures
  • Spectral density
  • Statistics of extremes