@article {11662, title = {Mean-of-order p reduced-bias extreme value index estimation under a third-order framework}, journal = {ExtremesExtremes}, volume = {19}, year = {2016}, note = {

Fundacao para a Ciencia e a Tecnologia (FCT) - UID/MAT/00006/2013 (CEA/UL) ; UID/MAT/00297/2013 (CMA/UNL)COST Action - IC1408
KU Leuven project - HSTRT/14/001

}, month = {2016/12/1}, pages = {561 - 589}, abstract = {

Reduced-bias versions of a very simple generalization of the {\textquoteleft}classical{\textquoteright} Hill estimator of a positive extreme value index (EVI) are put forward. The Hill estimator can be regarded as the logarithm of the mean-of-order-0 of a certain set of statistics. Instead of such a geometric mean, it is sensible to consider the mean-of-order-p (MOP) of those statistics, with p real. Under a third-order framework, the asymptotic behaviour of the MOP, optimal MOP and associated reduced-bias classes of EVI-estimators is derived. Information on the dominant non-null asymptotic bias is also provided so that we can deal with an asymptotic comparison at optimal levels of some of those classes. Large-scale Monte-Carlo simulation experiments are undertaken to provide finite sample comparisons.Reduced-bias versions of a very simple generalization of the {\textquoteleft}classical{\textquoteright} Hill estimator of a positive extreme value index (EVI) are put forward. The Hill estimator can be regarded as the logarithm of the mean-of-order-0 of a certain set of statistics. Instead of such a geometric mean, it is sensible to consider the mean-of-order-p (MOP) of those statistics, with p real. Under a third-order framework, the asymptotic behaviour of the MOP, optimal MOP and associated reduced-bias classes of EVI-estimators is derived. Information on the dominant non-null asymptotic bias is also provided so that we can deal with an asymptotic comparison at optimal levels of some of those classes. Large-scale Monte-Carlo simulation experiments are undertaken to provide finite sample comparisons.

}, keywords = {bias estimation, heavy tails, Optimal levels, Semi-parametric reduced-bias estimation, Statistics of extremes}, isbn = {1386-1999}, url = {http://www.scopus.com/inward/record.url?scp=84975457832\&partnerID=8YFLogxK}, author = {Caeiro, Frederico and Gomes, M. Ivette and Beirlant,Jan and de Wet,Tertius} }