论文标题
使用极端U统计量的尾部推理
Tail inference using extreme U-statistics
论文作者
论文摘要
当U统计量的内核具有高度时，就会出现极端U统计量，但仅通过少量的最高级统计数据取决于其论点。随着U统计的内核度随样本量增长到无穷大，根据此类统计数据构建的估计量形成了一个中间家庭，在块最大值中构建的统计范围与极值分析中的限制性群体和阈值阈值框架。建立了基于位置尺度不变内核的极端U统计量的渐近正态性。尽管渐进差异与Hájek投影之一相吻合，但该证据不仅是考虑Hoeffding差异分解的第一个术语。我们根据三个最高阶段统计数据提出一个内核，这导致了类似于Pickands估算器的极值指数的位置尺度不变估计器。这种极端的选择和u-估计剂在渐近上是正常的，其有限样本的性能与伪最大的可能性估计量具有竞争力。
Extreme U-statistics arise when the kernel of a U-statistic has a high degree but depends only on its arguments through a small number of top order statistics. As the kernel degree of the U-statistic grows to infinity with the sample size, estimators built out of such statistics form an intermediate family in between those constructed in the block maxima and peaks-over-threshold frameworks in extreme value analysis. The asymptotic normality of extreme U-statistics based on location-scale invariant kernels is established. Although the asymptotic variance coincides with the one of the Hájek projection, the proof goes beyond considering the first term in Hoeffding's variance decomposition. We propose a kernel depending on the three highest order statistics leading to a location-scale invariant estimator of the extreme value index resembling the Pickands estimator. This extreme Pickands U-estimator is asymptotically normal and its finite-sample performance is competitive with that of the pseudo-maximum likelihood estimator.
