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Local Estimation of the Conditional Stable Tail Dependence Function

Author

Listed:
  • Mikael Escobar‐Bach
  • Yuri Goegebeur
  • Armelle Guillou

Abstract

We consider the local estimation of the stable tail dependence function when a random covariate is observed together with the variables of main interest. Our estimator is a weighted version of the empirical estimator adapted to the covariate framework. We provide the main asymptotic properties of our estimator, when properly normalized, in particular the convergence of the empirical process towards a tight centred Gaussian process. The finite sample performance of our estimator is illustrated on a small simulation study and on a dataset of air pollution measurements.

Suggested Citation

  • Mikael Escobar‐Bach & Yuri Goegebeur & Armelle Guillou, 2018. "Local Estimation of the Conditional Stable Tail Dependence Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 590-617, September.
    • Handle: RePEc:bla:scjsta:v:45:y:2018:i:3:p:590-617
    DOI: 10.1111/sjos.12315
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    Cited by:

    1. Goegebeur, Yuri & Guillou, Armelle & Qin, Jing, 2021. "Extreme value estimation of the conditional risk premium in reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 68-80.
    2. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2023. "A Weissman-type estimator of the conditional marginal expected shortfall," Econometrics and Statistics, Elsevier, vol. 27(C), pages 173-196.
    3. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2023. "Nonparametric estimation of conditional marginal excess moments," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    4. Yuri Goegebeur & Armelle Guillou & Jing Qin, 2023. "Robust estimation of the conditional stable tail dependence function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 201-231, April.

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