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Spectral Density Ratio Models for Multivariate Extremes

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  • Miguel de Carvalho
  • Anthony C. Davison

Abstract

The modeling of multivariate extremes has received increasing recent attention because of its importance in risk assessment. In classical statistics of extremes, the joint distribution of two or more extremes has a nonparametric form, subject to moment constraints. This article develops a semiparametric model for the situation where several multivariate extremal distributions are linked through the action of a covariate on an unspecified baseline distribution, through a so-called density ratio model. Theoretical and numerical aspects of empirical likelihood inference for this model are discussed, and an application is given to pairs of extreme forest temperatures. Supplementary materials for this article are available online.

Suggested Citation

  • Miguel de Carvalho & Anthony C. Davison, 2014. "Spectral Density Ratio Models for Multivariate Extremes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 764-776, June.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:506:p:764-776
    DOI: 10.1080/01621459.2013.872651
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    Cited by:

    1. Mao, Shanjun & Fan, Xiaodan & Hu, Jie, 2021. "Correlation for tree-shaped datasets and its Bayesian estimation," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    2. Hanson, Timothy E. & de Carvalho, Miguel & Chen, Yuhui, 2017. "Bernstein polynomial angular densities of multivariate extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 60-66.
    3. Zhang, Archer Gong & Chen, Jiahua, 2022. "Density ratio model with data-adaptive basis function," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    4. Raphaël Huser & Marc G. Genton, 2016. "Non-Stationary Dependence Structures for Spatial Extremes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 470-491, September.
    5. Mhalla, Linda & Chavez-Demoulin, Valérie & Naveau, Philippe, 2017. "Non-linear models for extremal dependence," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 49-66.
    6. Wang, Chunlin & Marriott, Paul & Li, Pengfei, 2017. "Testing homogeneity for multiple nonnegative distributions with excess zero observations," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 146-157.
    7. Pengfei Li & Yukun Liu & Jing Qin, 2017. "Semiparametric Inference in a Genetic Mixture Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1250-1260, July.
    8. Daniela Castro Camilo & Miguel de Carvalho & Jennifer Wadsworth, 2017. "Time-Varying Extreme Value Dependence with Application to Leading European Stock Markets," Papers 1709.01198, arXiv.org.

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