An efficient semiparametric maxima estimator of the extremal index

Abstract The extremal index θ , a measure of the degree of local dependence in the extremes of a stationary process, plays an important role in extreme value analyses. We estimate θ semiparametrically, using the relationship between the distribution of block maxima and the marginal distribution of a process to define a semiparametric model. We show that these semiparametric estimators are simpler and substantially more efficient than their parametric counterparts. We seek to improve efficiency further using maxima over sliding blocks. A simulation study shows that the semiparametric estimators are competitive with the leading estimators. An application to seasurge heights combines inferences about θ with a standard extreme value analysis of block maxima to estimate marginal quantiles.