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Asymptotically unbiased estimation of the extreme value index under random censoring

Martin Bladt et al.

Insurance: Mathematics & Economics2026https://doi.org/10.1016/j.insmatheco.2026.103225article
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Abstract

We consider bias-corrected estimation of the extreme value index of Pareto-type loss distributions in the censoring framework. The initial estimator is based on a Kaplan–Meier integral from which we remove the bias under a second-order framework. This estimator depends on a suitable external estimation of second-order parameters, which is also discussed. The weak convergence of the bias-corrected estimator is established. It has the nice property of having the same asymptotic variance as the initial estimator. This feature is illustrated in a simulation study where our estimator is compared to alternatives already introduced in the literature. Finally, our methodology is applied to a French non-life insurance dataset.

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https://doi.org/https://doi.org/10.1016/j.insmatheco.2026.103225

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@article{martin2026,
  title        = {{Asymptotically unbiased estimation of the extreme value index under random censoring}},
  author       = {Martin Bladt et al.},
  journal      = {Insurance: Mathematics & Economics},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1016/j.insmatheco.2026.103225},
}

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Asymptotically unbiased estimation of the extreme value index under random censoring

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