Asymptotically unbiased estimation of the extreme value index under random censoring
针对删失框架下帕累托型损失分布的极值指数，提出一种基于Kaplan-Meier积分的偏差校正估计量，具有与初始估计量相同的渐近方差，并通过模拟和法国非寿险数据验证其性能。
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.