论文标题
滑动块的渐近学估算罕见事件的估计值
Asymptotics for sliding blocks estimators of rare events
论文作者
论文摘要
Drees andRootzén（2010）已经建立了一类统计经验过程的限制定理，这些过程对于时间序列的极端价值分析很有用，但不适用于滑动块的统计数据，包括所谓的运行估计器。我们将这些结果推广到经验过程，这些过程涵盖了Drees和Rootzén（2010）考虑的类别以及滑动块统计的过程。使用这种方法，可以在统一框架中分析不同类型的统计信息。我们表明，基于滑动块的统计数据在渐近条件下是渐近正常的，在相当温和的条件下，基于分离块的相应估计器的渐近方差小于或等于或等于渐近方差。最后，将一般理论应用于极端指数的三个众所周知的估计量。事实证明，它们都具有相同的限制分布，这一事实在文献中已经忽略了。
Drees and Rootzén (2010) have established limit theorems for a general class of empirical processes of statistics that are useful for the extreme value analysis of time series, but do not apply to statistics of sliding blocks, including so-called runs estimators. We generalize these results to empirical processes which cover both the class considered by Drees and Rootzén (2010) and processes of sliding blocks statistics. Using this approach, one can analyze different types of statistics in a unified framework. We show that statistics based on sliding blocks are asymptotically normal with an asymptotic variance which, under rather mild conditions, is smaller than or equal to the asymptotic variance of the corresponding estimator based on disjoint blocks. Finally, the general theory is applied to three well-known estimators of the extremal index. It turns out that they all have the same limit distribution, a fact which has so far been overlooked in the literature.
