Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study

• Autor(a) principal: Caeiro, Frederico
• Data de Publicação: 2020
• Outros Autores: Henriques-Rodrigues, Lígia, Gomes, M. Ivette, Cabral, Ivanilda
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/33024; https://doi.org/Caeiro, F, Henriques-Rodrigues, L, Gomes, MI, Cabral, I. Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study. Comp and Math Methods. 2020; 2:e1101. https://doi.org/10.1002/cmm4.1101; https://doi.org/10.1002/cmm4.1101
• topic: asymptotic bias; extreme value index; minimum asymptotic bias; semiparametric estimation; statistic of extremes

In extreme value (EV) analysis, the EV index (EVI), , is the primary parame- ter of extreme events. In this work, we consider positive, that is, we assume that F is heavy tailed. Classical tail parameters estimators, such as the Hill, the Moments, or the Weissman estimators, are usually asymptotically biased. Con- sequently, those estimators are quite sensitive to the number of upper order statistics used in the estimation. Minimum-variance reduced-bias (RB) estima- tors have enabled us to remove the dominant component of asymptotic bias without increasing the asymptotic variance of the new estimators. The purpose of this paper is to study a new minimum-variance RB estimator of the EVI. Under adequate conditions, we prove their nondegenerate asymptotic behavior. More- over, an asymptotic and empirical comparison with other minimum-variance RB estimators from the literature is also provided. Our results show that the proposed new estimator has the potential to be very useful in practice.