We consider removing lower order statistics from the classical Hill estimator in extreme value statistics, and compensating for it by rescaling the remaining terms. Trajectories of these trimmed statistics as a function of the extent of trimming turn out to be quite flat near the optimal threshold value. For the regularly varying case, the classical threshold selection problem in tail estimation is then revisited, both visually via trimmed Hill plots and, for the Hall class, also mathematically via minimizing the expected empirical variance. This leads to a simple threshold selection procedure for the classical Hill estimator which circumvents the estimation of some of the tail characteristics, a problem which is usually the bottleneck in threshold selection. As a by-product, we derive an alternative estimator of the tail index, which assigns more weight to large observations, and works particularly well for relatively lighter tails. A simple ratio statistic routine is suggested to evaluate the goodness of the implied selection of the threshold. We illustrate the favourable performance and the potential of the proposed method with simulation studies and real insurance data.

我们考虑从极值统计中的经典希尔估计器中删除低阶统计，并通过重新调整其余项来对其进行补偿。这些修整统计量的轨迹作为修整程度的函数证明在最佳阈值附近相当平坦。对于规则变化的情况，尾部估计中的经典阈值选择问题将通过修整后的希尔图在视觉上进行重新讨论，对于霍尔类，还会在数学上通过使期望的经验方差最小化而重新进行。这导致了经典的希尔估计器的简单阈值选择过程，该过程避免了某些尾部特征的估计，这通常是阈值选择的瓶颈。作为副产品，我们导出了尾部索引的替代估计量，可以将较大的权重分配给较大的观测值，并且对于相对较轻的尾巴特别有效。建议使用一个简单的比率统计例程来评估阈值隐含选择的优劣。我们通过仿真研究和真实的保险数据说明了该方法的优越性能和潜力。