A simple generalisation of the Hill estimator

M Fátima Brilhante, M Ivette Gomes, Dinis Pestana · 2013
DOI: 10.1016/j.csda.2012.07.019

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.

Reference

M Fátima Brilhante, M Ivette Gomes, Dinis Pestana “A simple generalisation of the Hill estimator” (2013) DOI: 10.1016/j.csda.2012.07.019

@Article{fatima2013,
  title = {A simple generalisation of the Hill estimator},
  volume = {57},
  issn = {0167-9473},
  url = {http://www.sciencedirect.com/science/article/pii/S0167947312002939},
  doi = {10.1016/j.csda.2012.07.019},
  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.},
  language = {en},
  number = {1},
  urldate = {2020-06-27},
  journal = {Computational Statistics \& Data Analysis},
  author = {Fátima Brilhante, M and Ivette Gomes, M and Pestana, Dinis},
  month = {jan},
  year = {2013},
  keywords = {Bias estimation, Bootstrap methodology, Heavy tails, Optimal levels, Semi-parametric estimation, Statistics of extremes},
  pages = {518--535}
}