Please use this identifier to cite or link to this item: http://hdl.handle.net/10174/33586

Title: A Generalized Mean Under a Non-Regular Framework and Extreme Value Index Estimation
Authors: Gomes, Maria Ivette
Henriques-Rodrigues, Lígia
Pestana, Dinis
Editors: Zafeiris, Konstantinos N.
Skiadas, Christos H.
Dimotikalis, Yiannis
Karagrigoriou, Alex
Karagrigoriou-Vonta, Christiana
Issue Date: Oct-2022
Publisher: iSTE and Wiley
Citation: Gomes, M.I., Henriques-Rodrigues, L. & Pestana, D. (2022). A Generalized Mean Under a Non-Regular Framework and Extreme Value Index Estimation. In K.N. Zafeiris, Y. Dimotikalis, C.H. Skiadas, A. Karagrigoriou and C. Karagrigoriou-Vonta (Eds.), Data Analysis and Related Applications 2, Volume 10—Big Data, Artificial Intelligence and Data Analysis, SET Coordinate by Jacques Janssen, ISBN: 9781786307729, iSTE Wiley, Part 3, Chapter 16, 237-250. https://www.iste.co.uk/book.php?id=1928
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 behavior 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. The results are illustrated on the basis of large-scale simulation studies. An algorithm providing an almost degenerate MOp EVI-estimation is suggested.
URI: http://hdl.handle.net/10174/33586
ISBN: 9781786307729
Type: bookPart
Appears in Collections:CIMA - Publicações - Capítulos de Livros

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