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Robust estimation of the Pickands dependence function under random right censoring

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  • Goegebeur, Yuri
  • Guillou, Armelle
  • Qin, Jing

Abstract

We consider robust nonparametric estimation of the Pickands dependence function under random right censoring. The estimator is obtained by applying the minimum density power divergence criterion to properly transformed bivariate observations. The asymptotic properties are investigated by making use of results for Kaplan–Meier integrals. We investigate the finite sample properties of the proposed estimator with a simulation experiment and illustrate its practical applicability on a dataset of insurance indemnity losses.

Suggested Citation

  • Goegebeur, Yuri & Guillou, Armelle & Qin, Jing, 2019. "Robust estimation of the Pickands dependence function under random right censoring," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 101-114.
    • Handle: RePEc:eee:insuma:v:87:y:2019:i:c:p:101-114
    DOI: 10.1016/j.insmatheco.2019.03.008
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    References listed on IDEAS

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    1. Severini,Thomas A., 2005. "Elements of Distribution Theory," Cambridge Books, Cambridge University Press, number 9780521844727, October.
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    4. 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.
    5. Beirlant, J. & Bardoutsos, A. & de Wet, T. & Gijbels, I., 2016. "Bias reduced tail estimation for censored Pareto type distributions," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 78-88.
    6. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
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