论文标题
在极端LP块集群推理的渐近学上
On the asymptotics of extremal lp-blocks cluster inference
论文作者
论文摘要
极端发生在固定时间序列中，以短期序列变化，并以几个大观测（称为极端块）发生。我们研究了群集统计数据，总结了作用在这些极端块上的功能的行为。群集统计的示例是极端指数，群集大小概率和其他集群指数。我们工作的目的是双重的。首先，我们指出，基于较大的LP-norms的连续观测值，对于p <0，块估计量的渐差正态性，p <0。case p = $α$，其中$α$> 0是时间序列的尾巴索引，因此具有特定的良好属性，因此我们分析了blocks估计器在使用$α$α$α$α$α$α$α$α$α$α$α$α$α$α估计器时分析。其次，我们验证在经典模型（例如线性模型和随机复发方程的解决方案）上所需的条件。关于线性模型，我们证明基于经典索引群集的渐近方差为HSING T. [26]首次猜想。我们说明了关于模拟的发现。
Extremes occur in stationary regularly varying time series as short periods with several large observations, known as extremal blocks. We study cluster statistics summarizing the behavior of functions acting on these extremal blocks. Examples of cluster statistics are the extremal index, cluster size probabilities, and other cluster indices. The purpose of our work is twofold. First, we state the asymptotic normality of block estimators for cluster inference based on consecutive observations with large lp-norms, for p < 0. The case p=$α$, where $α$ > 0 is the tail index of the time series, has specific nice properties thus we analyze the asymptotic of blocks estimators when approximating $α$ using the Hill estimator. Second, we verify the conditions we require on classical models such as linear models and solutions of stochastic recurrence equations. Regarding linear models, we prove that the asymptotic variance of classical index cluster-based estimators is null as first conjectured in Hsing T. [26]. We illustrate our findings on simulations.
