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Title: Reduced-bias location-invariant extreme value index estimation: a simulation study
Author: Gomes, M. Ivette
Henriques-Rodrigues, Lígia
Miranda, M. Cristina
Keywords: Adaptive choice
Bias reduction
Extreme value index
Semi-parametric location/scale invariant estimation
Statistics of extremes
Issue Date: Feb-2011
Publisher: Taylor & Francis
Abstract: In this article, we deal with semi-parametric corrected-bias estimation of a positive extreme value index (EVI), the primary parameter in statistics of extremes. Under such a context, the classical EVI-estimators are the Hill estimators, based on any intermediate number k of top-order statistics. But these EVI-estimators are not location-invariant, contrarily to the PORT-Hill estimators, which depend on an extra tuning parameter q, with 0 ≤ q < 1, and where PORT stands for peaks over random threshold. On the basis of second-order minimum-variance reduced-bias (MVRB) EVI-estimators, we shall here consider PORT-MVRB EVI-estimators. Due to the stability on k of the MVRB EVI-estimates, we propose the use of a heuristic algorithm, for the adaptive choice of k and q, based on the bias pattern of the estimators as a function of k. Applications in the fields of insurance and finance will be provided.
Peer review: yes
DOI: 10.1080/03610918.2010.543297
ISSN: 0361-0918
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Appears in Collections:ISCA-UA - Artigos

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