“Asymptotically Unbiased” Estimators of the Tail Index Based on External Estimation of the Second Order Parameter

In this paper we shall deal with the asymptotic and finite sample properties of “asymptotically unbiased” estimators of the tail index γ, based on “external” adequate estimators of the second order parameter ρ. The behavior of the ρ-estimator considered has indeed a high impact on the distributional properties of the final estimator of γ, and must be carefully chosen. As a by-product of the final study we present also the finite sample properties of a few ρ-estimators available in the literature.