ABSTRACT
Under a convenient third-order framework, the asymptotic distributional behavior of a class of location-invariant reduced-bias tail index estimators is derived. Such a class is based on the PORT methodology, with PORT standing for peaks over random thresholds, and combines a PORT version of one of the pioneering classes of minimum-variance reduced-bias tail index estimators with two classes of location invariant estimators of adequate second-order parameters, recently introduced in the literature. An application to simulated Student-t data and to the log-exchange rates of the Euro against the U.S. dollar and the Euro against the GB pound is also provided.
AMS SUBJECT CLASSIFICATION:
Funding
Research partially supported by Fundação para a Ciência e Tecnologia (FCT), project UID/MAT/00006/2013 (CEA/UL).