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Title: Non-reduced versus reduced-bias estimators of the extreme value index: Efficiency and robustness Authors:  Ivette Gomes - FCiencias.ID, Universidade de Lisboa and CEAUL (Portugal) [presenting]
Abstract: The \textit{extreme value index} (EVI) is the primary parameter of extreme events. The EVI is used to characterize the tail behavior of a distribution, and it helps to indicate the size and frequency of certain extreme events under a given probability model: for large events, the bigger the EVI is, the heavier is the right-tail of the underlying parent distribution. The Lehmer mean of order $p$ of the $k$ log-excesses over the $k+1$-th upper order statistic has been recently considered in the literature for the estimation of a positive EVI, associated with large extreme events. Such a Lehmer mean of order $p$ generalizes the arithmetic mean $(p=1)$, the classical Hill estimator of a positive EVI, and for $p>1$ has revealed to be very competitive for small values of the EVI, comparing favorably with one the simplest classes of reduced-bias EVI-estimators, a corrected-Hill estimator. Now, the comparison to other EVI-estimators is performed, and some information on the robustness of such a general class is provided, including its resistance to possible contamination by outliers.