Use of censored distribution in the intervals estimator of the extremal index

From the theory it follows that the local dependence in a stationary series causes clustering of extreme values. Hence, the inference for extremes typically requires proper identification of clusters of high threshold exceedances and estimation of the extremal index which is the primary measure of the local dependence. An intervals estimator of the extremal index based on the distribution of interexceedances times has been previously introduced. Direct application of the limiting distribution to interexceedances times of a stationary series may cause the intervals estimator to be biased toward independence. Several modifications have been proposed including the $K$-gaps likelihood estimator, where $K$ determines the intra- and intercluster spacings. The aim is to introduce a new estimator of the extremal index based on censored distributions that can be viewed as an alternative to the $K$-gaps estimator without using fixed replacements of the intracluster spacings. Properties of the estimator are studied using simulations. The main benefit lies in reducing the bias of the estimates, especially when large clusters are present in the series.