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A couple of non reduced bias generalized means in extreme value theory
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Orientador(es)
Resumo(s)
Lehmer’s mean-of-order p (Lp) generalizes the arithmetic mean, and Lp extreme value index (EVI)-estimators can be easily built, as a generalization of the classical Hill EVI-estimators. Apart from a reference to the asymptotic behaviour of this class of estimators, an asymptotic comparison, at optimal levels, of the members of such a class reveals that for the optimal (p, k) in the sense of minimal mean square error, with k the number of top order statistics involved in the estimation, they are able to overall outperform a recent and promising generalization of the Hill EVI-estimator, related to the power mean, also known as Hölder’s mean-of-order-p. A further comparison with other ‘classical’ non-reduced-bias estimators still reveals the competitiveness of this class of EVI-estimators.
Descrição
The authors are grateful to the Editor and Referees for their careful reviews and helpful suggestions, which have improved the final version of this article. This work has been supported by COST Action IC1408—CroNos and by FCT—Fundacão para a Ciência e a Tecnologia, Portugal, UID/MAT/0297/2013 (CMA/UNL).
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© 2020, National Statistical Institute. All rights reserved.
Palavras-chave
Heavy tails Optimal tuning parameters Semi-parametric estimation Statistical extreme value theory Statistics and Probability