A simple generalisation of the Hill estimator

Autor:	M. Fátima Brilhante, Dinis Pestana, M. Ivette Gomes
Rok vydání:	2013
Předmět:	Statistics and Probability Class (set theory) Logarithm Applied Mathematics Estimator Set (abstract data type) Computational Mathematics Computational Theory and Mathematics Bias of an estimator Simple (abstract algebra) Statistics Order (group theory) Applied mathematics Geometric mean Mathematics
Zdroj:	Computational Statistics & Data Analysis. 57:518-535
ISSN:	0167-9473
DOI:	10.1016/j.csda.2012.07.019
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e88c1da5e1f227f181245037a81d9636 https://doi.org/10.1016/j.csda.2012.07.019 Zobrazit plný text záznamu Full Text from ScienceDirect