Under stationarity and weak dependence, the statistical significance and the estimation of the extremal index are considered. It is shown that the distribution of the sample maximum can be uniformly approximated given the extremal index and the marginal distribution as the sample size increases. An adaptive procedure is proposed for estimating the extremal index. The procedure is shown to be asymptotically optimal in a class of estimators.
"Extremal Index Estimation for a Weakly Dependent Stationary Sequence." Ann. Statist. 21 (4) 2043 - 2071, December, 1993. https://doi.org/10.1214/aos/1176349409