When analysing extreme values, two alternative statistical approaches have historically been held in contention: the block maxima method (or annual maxima method, spurred by hydrological applications) and the peaks-over-threshold. Clamoured amongst statisticians as wasteful of potentially informative data, the block maxima method gradually fell into disfavour whilst peaks-over-threshold-based methodologies climbed to the centre stage of extreme value statistics. This paper devises a hybrid method which reconciles these two hitherto disconnected approaches. Appealing in its simplicity, our main result introduces a new universality class of extreme value distributions that discards the customary requirement of a sufficiently large block size for the plausible block maxima-fit to an extreme value distribution. Natural extensions to dependent and/or non-stationary settings are mapped out. We advocate that inference should be drawn solely on larger block maxima, from which practice the mainstream peaks-over-threshold methodology coalesces: the asymptotic properties of the hybrid-Hill estimator herald more than its efficiency, but rather that a fully-fledged unified semi-parametric stream of statistics for extreme values is viable. A reduced-bias off-shoot of the hybrid-Hill estimator provably outclasses the incumbent maximum likelihood estimation that relies on a numerical fit to the entire sample of block maxima.

翻译：在分析极值时，历史上存在两种相互对立的统计方法：块最大值法（或称年最大值法，源于水文应用）以及超阈值峰值法。由于统计学家们批评块最大值法浪费了潜在的信息数据，该方法逐渐失宠，而基于超阈值峰值的方法则登上了极值统计学的中心舞台。本文设计了一种混合方法，将这两种迄今相互割裂的路径统一起来。我们的主要结果引入了一类新的极值分布普适性类别，其简洁性颇具吸引力，它摒弃了传统上要求块大小必须足够大才能使块最大值拟合到极值分布这一条件。我们进一步勾勒了该方法向相依性和/或非平稳性场景的自然扩展。我们主张，推断应仅基于较大的块最大值进行，而主流超阈值峰值方法正是由此实践融合而来：混合Hill估计器的渐近性质预示的不仅是其高效性，更表明一个完整的、统一的极值半参数统计流是可行的。混合Hill估计器的一个减偏衍生版本，在理论上优于当前依赖于对整个块最大值样本进行数值拟合的最大似然估计。