Threshold selection plays a key role in various aspects of statistical inference of rare events. In this work, two new threshold selection methods are introduced. The first approach measures the fit of the exponential approximation above a threshold and achieves good performance in small samples. The second method smoothly estimates the asymptotic mean squared error of the Hill estimator and performs consistently well over a wide range of processes. Both methods are analyzed theoretically, compared to existing procedures in an extensive simulation study and applied to a dataset of financial losses, where the underlying extreme value index is assumed to vary over time.

阈值选择在稀有事件的统计推断的各个方面发挥着关键作用。在这项工作中，引入了两种新的阈值选择方法。第一种方法在阈值以上测量指数逼近的拟合，并在小样本中获得良好的性能。第二种方法可以平滑地估计Hill估计器的渐进均方误差，并且在广泛的过程中均能始终如一地表现良好。从理论上分析了这两种方法，并与广泛的模拟研究中的现有程序进行了比较，并将它们应用于财务损失数据集，在该数据集中，潜在的极值指数随时间变化。