Extreme Value Theory and Dependence

摘要

The purpose of this paper is to give a very brief account of some of the essential ideas underlying classical extreme value theory, and to see how these are used (modified as necessary) for dependent cases. In particular it will be shown how the classical theory still applies for moderately dependent stationary sequences, but that under higher local dependence, clustering of high values occurs, requiring modifications of the theory especially as it involves order statistics other than the maximum. Underlying concepts (especially point process convergence results) are emphasized. (Author)