Abstract
In this paper, we discuss an algorithm for the adaptive estimation of a positive extreme value index, γ, the primary parameter in Statistics of Extremes. Apart from the classical extreme value index estimators, we suggest the consideration of associated second-order corrected-bias estimators, and propose the use of resampling-based computer-intensive methods for an asymptotically consistent choice of the thresholds to use in the adaptive estimation of γ. The algorithm is described for a classical γ-estimator and associated corrected-bias estimator, but it can work similarly for the estimation of other parameters of extreme events, like a high quantile, the probability of exceedance or the return period of a high level.
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Research partially supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, project PEst-OE/MAT/UI0006/2011 and PTDC/FEDER.
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Gomes, M.I., Figueiredo, F. & Neves, M.M. Adaptive estimation of heavy right tails: resampling-based methods in action. Extremes 15, 463–489 (2012). https://doi.org/10.1007/s10687-011-0146-6
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DOI: https://doi.org/10.1007/s10687-011-0146-6