Abstract
A simple generalisation of the classical Hill estimator of a positive extreme value index (EVI) has been recently introduced in the literature. Indeed, the Hill estimator can be regarded as the logarithm of the geometric mean, or equivalently the logarithm of the mean of order p = 0, of a set of adequate statistics. Instead of such a geometric mean, it is thus sensible to consider the mean of order p (MOP) of those statistics, with p ≥ 0. In this paper, a small-scale simulation study and a closer look at the asymptotic behaviour at optimal levels of the class of MOP EVI-estimators enable us to better understand their properties and to suggest simple adaptive EVI-estimates.
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Acknowledgements
Research partially supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, project PEst-OE/MAT/UI0006/2011, and EXTREMA, PTDC/FEDER.
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Brilhante, M.F., Gomes, M.I., Pestana, D. (2014). The MOP EVI-Estimator Revisited. In: Pacheco, A., Santos, R., Oliveira, M., Paulino, C. (eds) New Advances in Statistical Modeling and Applications. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-05323-3_16
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DOI: https://doi.org/10.1007/978-3-319-05323-3_16
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