A simple generalisation of the Hill estimator

M. Fátima Brilhante, M. Ivette Gomes and Dinis Pestana

Computational Statistics & Data Analysis, 2013, vol. 57, issue 1, 518-535

Abstract: The classical Hill estimator of a positive extreme value index (EVI) can be regarded as the logarithm of the geometric mean, or equivalently the logarithm of the mean of order p=0, of a set of adequate statistics. A simple generalisation of the Hill estimator is now proposed, considering a more general mean of order p≥0 of the same statistics. Apart from the derivation of the asymptotic behaviour of this new class of EVI-estimators, an asymptotic comparison, at optimal levels, of the members of such class and other known EVI-estimators is undertaken. An algorithm for an adaptive estimation of the tuning parameters under play is also provided. A large-scale simulation study and an application to simulated and real data are developed.

Keywords: Bias estimation; Bootstrap methodology; Heavy tails; Optimal levels; Semi-parametric estimation; Statistics of extremes (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:57:y:2013:i:1:p:518-535

DOI: 10.1016/j.csda.2012.07.019

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