相依极值事件序列的积分周期图
The integrated periodogram of a dependent extremal event sequence
摘要：
我们研究了由一系列相关极值事件的指示函数计算的积分周期图的渐近性质。欧几里得空间中的一个事件如果发生在远离原点的地方，那么它就是极端的。我们使用一个定期的变化条件的基础上的平稳序列，使这些概念精确。我们的主要结果是一个泛函中心极限定理的积分周期图的指示函数的相关极值事件。极限过程是一个连续的高斯过程，其协方差结构一般是陌生的，但在iid的情况下，布朗桥出现。在一般情况下，我们提出了一个平稳的自助程序近似的极限过程的分布。开发的理论可以用来构建经典的拟合优度检验，如Grenander-Rosenblatt和Cramér-von Mises检验，这些检验仅基于样本中的极值。我们将检验统计量应用于模拟和真实数据。
英文摘要：
We investigate the asymptotic properties of the integrated periodogram calculated from a sequence of indicator functions of dependent extremal events. An event in Euclidean space is extreme if it occurs far away from the origin. We use a regular variation condition on the underlying stationary sequence to make these notions precise. Our main result is a functional central limit theorem for the integrated periodogram of the indicator functions of dependent extremal events. The limiting process is a continuous Gaussian process whose covari- ance structure is in general unfamiliar, but in the iid case a Brownian bridge appears. In the general case, we propose a stationary bootstrap procedure for approximating the distribution of the limiting process. The developed theory can be used to construct classical goodness-of-fit tests such as the Grenander- Rosenblatt and Cramér-von Mises tests which are based only on the extremes in the sample. We apply the test statistics to simulated and real-life data.
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