## Reference

M Fátima Brilhante, M Ivette Gomes, Dinis Pestana“A simple generalisation of the Hill estimator” (2013) // Computational Statistics & Data Analysis. Vol. 57. No 1. Pp. 518–535. 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.

## Bib

```
@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}
}
```