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Bias-corrected estimation of stable tail dependence function

Author

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  • Beirlant, Jan
  • Escobar-Bach, Mikael
  • Goegebeur, Yuri
  • Guillou, Armelle

Abstract

We consider the estimation of the stable tail dependence function. We propose a bias-corrected estimator and we establish its asymptotic behaviour under suitable assumptions. The finite sample performance of the proposed estimator is evaluated by means of an extensive simulation study where a comparison with alternatives from the recent literature is provided.

Suggested Citation

  • Beirlant, Jan & Escobar-Bach, Mikael & Goegebeur, Yuri & Guillou, Armelle, 2016. "Bias-corrected estimation of stable tail dependence function," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 453-466.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:453-466
    DOI: 10.1016/j.jmva.2015.10.006
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    References listed on IDEAS

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    1. Beirlant, J. & Dierckx, G. & Guillou, A., 2011. "Bias-reduced estimators for bivariate tail modelling," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 18-26, July.
    2. Drees, Holger & Huang, Xin, 1998. "Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 25-47, January.
    3. Yuri Goegebeur & Armelle Guillou, 2013. "Asymptotically Unbiased Estimation of the Coefficient of Tail Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 174-189, March.
    4. Anthony W. Ledford & Jonathan A. Tawn, 1997. "Modelling Dependence within Joint Tail Regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 475-499.
    5. Holger Drees, 1998. "On Smooth Statistical Tail Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 187-210, March.
    6. M. Ivette Gomes & Laurens De Haan & Lígia Henriques Rodrigues, 2008. "Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 31-52, February.
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    Cited by:

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    2. Goix, Nicolas & Sabourin, Anne & Clémençon, Stephan, 2017. "Sparse representation of multivariate extremes with applications to anomaly detection," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 12-31.
    3. Mikael Escobar-Bach & Yuri Goegebeur & Armelle Guillou & Alexandre You, 2017. "Bias-corrected and robust estimation of the bivariate stable tail dependence function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 284-307, June.
    4. Falk, Michael & Padoan, Simone A. & Wisheckel, Florian, 2019. "Generalized Pareto copulas: A key to multivariate extremes," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    5. Cyril Bénézet & Emmanuel Gobet & Rodrigo Targino, 2021. "Transform MCMC schemes for sampling intractable factor copula models," Working Papers hal-03334526, HAL.
    6. Kiriliouk, Anna & Segers, Johan & Tafakori, Laleh, 2017. "An estimator of the stable tail dependence function based on the empirical beta copula," LIDAM Discussion Papers ISBA 2017028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Kiriliouk, Anna, 2020. "Hypothesis testing for tail dependence parameters on the boundary of the parameter space," Econometrics and Statistics, Elsevier, vol. 16(C), pages 121-135.
    8. Kiriliouk, Anna & Segers, Johan & Tafakori, Laleh, 2018. "An estimator of the stable tail dependence function based on the empirical beta copula," LIDAM Discussion Papers ISBA 2018029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Hu, Shuang & Peng, Zuoxiang & Segers, Johan, 2022. "Modelling multivariate extreme value distributions via Markov trees," LIDAM Discussion Papers ISBA 2022021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Goegebeur, Yuri & Guillou, Armelle & Qin, Jing, 2017. "On kernel estimation of the second order rate parameter in multivariate extreme value statistics," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 35-43.
    11. 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).
    12. Cyril Bénézet & Emmanuel Gobet & Rodrigo Targino, 2023. "Transform MCMC schemes for sampling intractable factor copula models," Post-Print hal-03334526, HAL.

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