论文标题
尾部指数和极端分数的均匀置信区间
On Uniform Confidence Intervals for the Tail Index and the Extreme Quantile
论文作者
论文摘要
本文提出了两个有关尾部指数和极端分位数均匀置信区间的结果。首先，我们表明，不可能构建一个长度优化的置信区间，以满足局部非参数尾部分布的正确均匀覆盖范围。其次，鉴于不可能的结果，我们构建了诚实的置信区间，通过在当地的非参数家族中纳入最严重的偏见，这些间隔是统一有效的。所提出的方法应用于国家卫生统计中心的模拟数据和国家重要统计数据的真实数据集。
This paper presents two results concerning uniform confidence intervals for the tail index and the extreme quantile. First, we show that it is impossible to construct a length-optimal confidence interval satisfying the correct uniform coverage over a local non-parametric family of tail distributions. Second, in light of the impossibility result, we construct honest confidence intervals that are uniformly valid by incorporating the worst-case bias in the local non-parametric family. The proposed method is applied to simulated data and a real data set of National Vital Statistics from National Center for Health Statistics.
