Title: Generalized means in statistical extreme value theory
Authors: Ivette Gomes - FCiencias.ID, Universidade de Lisboa and CEAUL (Portugal) [presenting]
Frederico Caeiro - NOVA.ID.FCT - Universidade Nova de Lisboa (Portugal)
Manuela Neves - University of Lisbon and CEAUL (Portugal)
Helena Penalva - ESCE-IPS and CEAUL-Universidade de Lisboa (Portugal)
Abstract: The focus is on Holder's and Lehmer's generalized mean-of-order-$p$ of adequate statistics based on the $k$ upper ordered observations associated with a stationary weakly dependent sample from a parent $F(\cdot)$. We are interested in the estimation of the extreme value index (EVI), the primary parameter in statistical extreme value theory (EVT) and related parameters, like the value-at-risk and the expected shortfall. The asymptotic behavior of the aforementioned classes of EVI-estimators enables their asymptotic comparison at optimal levels (k,p), in the sense of minimal mean square error. In the Monte-Carlo simulation study we further include the associated location-invariant PORT EVI-estimators, with PORT standing for peaks over random threshold.