A study of the jackknife method in the estimation of the extremal index

Abstract

Clustering of high values occurs in many real situations and affects inference on extremal events. For stationary dependent sequences, under general local and asymptotic dependence conditions, the degree of clustering is measured through a parameter called the extremal index. The estimation of extreme events or parameters is usually based on a k number of top order statistics or on the exceedances of a high threshold u and is very sensitive to either of these choices. In particular, the bias increases with a growing k and a decreasing u. The use of the Jackknife methodology may help reduce bias. We analyse this method through a simulation study applied to several estimators of the extremal index. An application to real data sets illustrates the results.