Asymptotically unbiased estimation of the extreme value index under random censoring

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.