A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach
复制标题
块极大值方法和峰值超过阈值方法之间的赛马比赛
作者：
Axel Bucher;Chen Zhou
经典极值统计包括两种基本方法：块极大值（BM）方法和峰值超过阈值（POT）方法。该领域的研究人员似乎普遍认为，POT方法比BM方法更有效地利用了极端观测值。我们从三个不同的角度阐述了这一讨论。首先，基于最近BM方法的理论结果，我们在i.i.d \场景中进行了理论比较。我们认为，数据生成过程可能有利于其中一种或另一种方法。其次，如果底层数据具有序列依赖性，我们认为方法的选择应该主要以最终的统计兴趣为指导：例如，POT更适合于分位数估计，而BM更适合于回报水平估计。最后，我们讨论了多变量观察的两种方法，并确定了未来研究的各种开放性。
Classical extreme value statistics consists of two fundamental approaches: the block maxima (BM) method and the peak-over-threshold (POT) approach. It seems to be general consensus among researchers in the field that the POT method makes use of extreme observations more efficiently than the BM method. We shed light on this discussion from three different perspectives. First, based on recent theoretical results for the BM approach, we provide a theoretical comparison in i.i.d.\ scenarios. We argue that the data generating process may favour either one or the other approach. Second, if the underlying data possesses serial dependence, we argue that the choice of a method should be primarily guided by the ultimate statistical interest: for instance, POT is preferable for quantile estimation, while BM is preferable for return level estimation. Finally, we discuss the two approaches for multivariate observations and identify various open ends for future research.