Location-invariant reduced-bias tail index estimation under a third-order framework

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.

KEYWORDS:

• Asymptotic properties
• heavy tails
• location/scale invariant estimation
• PORT methodology
• second-order parameters
• semiparametric estimation
• statistics of extremes

AMS SUBJECT CLASSIFICATION:

• Primary 62G32
• 62E20
• Secondary 65C05

Funding

Research partially supported by Fundação para a Ciência e Tecnologia (FCT), project UID/MAT/00006/2013 (CEA/UL).

Additional information

Funding

Research partially supported by Fundação para a Ciência e Tecnologia (FCT), project UID/MAT/00006/2013 (CEA/UL).