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B1726
Topic: Contributions in extreme values theory and applications Title: Searching for robust estimates of the extremal index Authors:  Manuela Souto de Miranda - University of Aveiro (Portugal)
Ivette Gomes - FCiencias.ID, Universidade de Lisboa and CEAUL (Portugal)
M Cristina Miranda - University of Aveiro (Portugal) [presenting]
Abstract: Many practical problems deal with extreme values above fixed levels and occurring in clusters of exceedances. The dependence among clusters is characterized by the extremal index of the process, which can be interpreted as the reciprocal of the clusters size mean. Several estimators of the extremal index have been proposed. They essentially differ in the identification of the groups. One of the most used proposals is known as the blocks estimator. Under specific local dependence and stationarity conditions the limit distribution of the number of exceedances follows a compound Poisson process where clusters occurrences are modeled by a Poisson distribution and clusters dimensions are determined by the process multiplicities. Since clusters dimension is generally reduced and can have a discrete asymmetric distribution, a robust version of the estimator should be based on a robust estimator of the mean clusters dimension taking into account those distributional properties. Assuming the Poisson distribution of the number of exceedances per cluster, the extremal index is estimated considering a robust Poisson regression estimate of the mean dimension of the clusters. The performance of the method is evaluated through the comparison of the results with those obtained when the observations are generated by a contaminated distribution.