Please use this identifier to cite or link to this item: http://hdl.handle.net/10174/33520

Title: A Generalized Mean Under a Non-Regular Framework and Extreme Value Index Estimation
Authors: Gomes, Maria Ivette
Henriques-Rodrigues, Lígia
Pestana, Dinis
Editors: Skiadas, Christos H
Keywords: Generalized Means
Non-regular Frameworks
Statistics of Extremes.
Issue Date: 2021
Publisher: Christos H Skiadas
Citation: Gomes, MI, Henriques-Rodrigues, L and Pestana, D. (2021). A Generalized Mean Under a Non-Regular Framework and Extreme Value Index Estimation. Proceedings ASMDA 2021: International Conference and Demographics 2021, Christos H Skiadas editor, pp. 317-328
Abstract: 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.
URI: http://www.asmda.es/images/!ASMDA2021_Conference_Proceedings_Book-compressed.pdf
http://hdl.handle.net/10174/33520
Type: article
Appears in Collections:CIMA - Artigos em Livros de Actas/Proceedings

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