Reduced-Bias Tail Index Estimators Under a Third-Order Framework

Abstract

In this article, we are interested in the comparison, under a third-order framework, of classes of second-order, reduced-bias tail index estimators, giving particular emphasis to minimum-variance reduced-bias estimators of the tail index γ. The full asymptotic distributional properties of the proposed classes are derived under a third-order framework and the estimators are compared with other alternatives, not only asymptotically, but also for finite samples through Monte Carlo techniques. An application to the log-exchange rates of the Euro against the USA Dollar is also provided.

Keywords:

• Bias estimation
• Heavy tails
• Semi-parametric estimation
• Statistics of extremes

Mathematics Subject Classification:

• Primary 62E20, 62G05, 62G32
• Secondary 62P05, 65C05

Acknowledgment

Research partially supported by FCT/POCTI, POCI, and PPCDT/FEDER.