Variants of the graph dependent model in extreme value theory |
| |
Authors: | Janes Galambos |
| |
Institution: | Department of Mathematics , Temple University , Philadelphia, pa, 19122 |
| |
Abstract: | With a set X1, X2, .... Xn n random variables, a graph is associated whose vertices are the integers 1,2,..., n and whose edges represent those pairs i and j for which the events {Xi>X} and {Xj>X} do not become “almost independent” for “large X”. With a variety of assumption on the edge set of the graph, the asymptotic distribution of the extremes of the Xj, when properly normalized, is determined. This refines the earlier result of the present author on this kind of dependence, and extends and unifies several known dependent extreme value models. |
| |
Keywords: | extremes dependent variables nonstatonary sequences Gaussian sequences mixing limiting distribution |
|
|