极值极限团簇大小分布的推断
Inference for the limiting cluster size distribution of extreme values
摘要：
在适当的长程相关条件下，平稳序列高能级时间归一化方差的极限点过程必然是复合泊松过程。通常情况下，不一致性出现在集群中。潜在的泊松点表示聚类位置，多重性对应于聚类大小。在本文中，我们介绍了估计的限制集群大小的概率，这是通过递归算法构建。我们得到的极值指数，它在确定集群位置的强度起着关键作用的估计。我们研究了估计量的渐近性质，并研究了它们在模拟数据上的有限样本行为。
英文摘要：
Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The underlying Poisson points represent the cluster positions and the multiplicities correspond to the cluster sizes. In the present paper we introduce estimators of the limiting cluster size probabilities, which are constructed through a recursive algorithm. We derive estimators of the extremal index which plays a key role in determining the intensity of cluster positions. We study the asymptotic properties of the estimators and investigate their finite sample behavior on simulated data.
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