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Modeling Extreme Events: Sample Fraction Adaptive Choice in Parameter Estimation

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Abstract

When modeling extreme events, there are a few primordial parameters, among which we refer to the extreme value index (EVI) and the extremal index (EI). Under a framework related to large values, the EVI measures the right tail weight of the underlying distribution and the EI characterizes the degree of local dependence in the extremes of a stationary sequence. Most of the semiparametric estimators of these parameters show the same type of behavior: nice asymptotic properties but a high variance for small values of k, the number of upper order statistics used in the estimation, and a high bias for large values of k. This brings a real need for the choice of k. Choosing some well-known estimators of those two parameters, we revisit the application of a heuristic algorithm for the adaptive choice of k. A simulation study illustrates the performance of the proposed algorithm.

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Correspondence to Dora Prata Gomes.

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Neves, M.M., Gomes, M.I., Figueiredo, F. et al. Modeling Extreme Events: Sample Fraction Adaptive Choice in Parameter Estimation. J Stat Theory Pract 9, 184–199 (2015). https://doi.org/10.1080/15598608.2014.890984

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  • DOI: https://doi.org/10.1080/15598608.2014.890984

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