An efficient semiparametric maxima estimator of the extremal index

TL;DR

This paper introduces a semiparametric maxima estimator for the extremal index, improving efficiency over parametric methods and demonstrating competitive performance through simulations and an application to sea-surge data.

Contribution

It proposes a new semiparametric estimator for the extremal index based on block maxima, which is simpler and more efficient than existing parametric estimators.

Findings

Semiparametric estimators are more efficient than parametric ones.

Sliding block maxima further improve estimator efficiency.

Estimator performs well in simulation and real data application.

Abstract

The extremal index $\theta$, 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 $\theta$ 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 sea-surge heights combines inferences about $\theta$ with a standard extreme value analysis of block maxima to estimate marginal quantiles.