New Reduced-bias Estimators of a Positive Extreme Value Index

Abstract

Noting that the classical Hill estimator of a positive extreme value index (EVI) is the logarithm of the mean of order-0 of a set of certain statistics, a more general class of EVI-estimators based on the mean of order-p (MOP), p ⩾ 0, of such statistics was recently introduced. The asymptotic behavior of the class of MOP EVI-estimators is reviewed, and compared to their reduced-bias MOP (RBMOP) and optimal RBMOP versions, which are suggested here and studied both asymptotically and for finite samples, through a large-scale simulation study. Applications to simulated datasets are also put forward.

Keywords:

• Bias estimation
• Heavy tails
• Monte Carlo simulation
• Semi-parametric reduced-bias estimation
• Statistics of extremes

Mathematics Subject Classification:

• Primary 62G32
• Secondary 65C05