A Generalized Mean Under a Non-Regular Framework and Extreme Value Index Estimation

• Autor(a) principal: Gomes, Maria Ivette
• Data de Publicação: 2021
• Outros Autores: Henriques-Rodrigues, Lígia, Pestana, Dinis
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/33520
• topic: Generalized Means; Non-regular Frameworks; Statistics of Extremes.

The Hill estimator, one of the most popular extreme value index (EVI) estimators under a heavy right-tail framework, i.e. for a positive EVI, here denoted by ξ, is an average of the log-excesses. Consequently, it can be regarded as the logarithm of the geometric mean or mean of order p = 0 of an adequate set of systematic statistics. We can thus more generally consider any real p, the mean of order p (MOp) of those same statistics and the associated MOp EVI-estimators, also called harmonic moment EVI-estimators. The normal asymptotic behaviour of these estimators has been obtained for p < 1/(2ξ), with consistency achieved for p < 1/ξ. The non-regular framework, i.e. the case p ≥ 1/(2ξ), will be now considered. Consistency is no longer achieved for p > 1/ξ, but an almost degenerate behavior appears for p = 1/ξ. Results are illustrated on the basis of large-scale simulation studies. An algorithm providing an almost degenerate MOp EVI-estimation is suggested.