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Title: On runs estimator of the extremal index: Dealing with clusters of exceedances with atypical dimensions Authors:  Manuela Souto de Miranda - University of Aveiro (Portugal) [presenting]
M Cristina Miranda - University of Aveiro (Portugal)
Ivette Gomes - FCiencias.ID, Universidade de Lisboa and CEAUL (Portugal)
Abstract: In Extreme Value Theory, the extremal index can have an important role when the exceedances above high fixed thresholds present a dependence structure, as it happens when they occur in clusters of exceedances. Under general conditions, the extremal index exists and is related to the clusters dimension in the limit distribution; since then, it coincides with the reciprocal of the mean clusters dimension. Several estimators have been proposed for that parameter, namely the runs estimator, which counts the number of exceedances that occur before a non--exceedance observation. A robust version of the runs estimator in the presence of atypical cluster sizes is investigated. The procedure is based on robust methods for counting processes and on the use of negative binomial regression. A simulation study illustrates the performance of the estimator when atypical cluster sizes are induced by contamination, considering different types of contamination.