论文标题
极端指数估计的阈值选择
Threshold selection for extremal index estimation
论文作者
论文摘要
我们提出了一种新的阈值选择方法，用于对随机过程的极端指数的非参数估计。提出了所谓的差异方法作为数据驱动的平滑工具，用于估计概率密度函数。现在，它已修改以选择极端索引估计器的阈值参数。为此，基于Cramér-Von Mises-Smirnov统计$ω^2 $的差异统计量的特定归一化是由$ K $最大订单统计数据而不是整个样本计算得出的。它的渐近分布为$ k \ to \ infty $被证明与$ω^2 $分布相同。后者分布的分位数用作差异值。得出了极端指数估计的收敛速率与差异法相结合。差异方法用作间隔的自动阈值选择和$ k-$差距估计器，并且可以应用于极端索引的其他估计器。
We propose a new threshold selection method for the nonparametric estimation of the extremal index of stochastic processes. The so-called discrepancy method was proposed as a data-driven smoothing tool for estimation of a probability density function. Now it is modified to select a threshold parameter of an extremal index estimator. To this end, a specific normalization of the discrepancy statistic based on the Cramér-von Mises-Smirnov statistic $ω^2$ is calculated by the $k$ largest order statistics instead of an entire sample. Its asymptotic distribution as $k\to\infty$ is proved to be the same as the $ω^2$-distribution. The quantiles of the latter distribution are used as discrepancy values. The rate of convergence of an extremal index estimate coupled with the discrepancy method is derived. The discrepancy method is used as an automatic threshold selection for the intervals and $K-$gaps estimators and it may be applied to other estimators of the extremal index.
