Nandagopalan S
Colorado State University, Fort Collins, CO 80523.
J Res Natl Inst Stand Technol. 1994 Jul-Aug;99(4):543-550. doi: 10.6028/jres.099.052.
The exceedance point process approach of Hsing et al. is extended to multivariate stationary sequences and some weak convergence results are obtained. It is well known that under general mixing assumptions, high level exceedances typically have a limiting Compound Poisson structure where multiple events are caused by the clustering of exceedances. In this paper we explore (a) the precise effect of such clustering on the limit, and (b) the relationship between point process convergence and the limiting behavior of maxima. Following this, the notion of multivariate extremal index is introduced which is shown to have properties analogous to its univariate counterpart. Two examples of bivariate moving average sequences are presented for which the extremal index is calculated in some special cases.
邢等人的超越点过程方法被扩展到多元平稳序列，并获得了一些弱收敛结果。众所周知，在一般混合假设下，高水平超越通常具有极限复合泊松结构，其中多个事件是由超越的聚类引起的。在本文中，我们探讨了（a）这种聚类对极限的精确影响，以及（b）点过程收敛与最大值极限行为之间的关系。在此之后，引入了多元极值指数的概念，结果表明它具有与其单变量对应物类似的性质。给出了二元移动平均序列的两个例子，并在一些特殊情况下计算了极值指数。
