An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index

• A robust and asymptotically unbiased estimator for the Pareto tail index is proposed.
• Consistency and asymptotic normality is established.
• Simulations and comparison to alternatives are proposed.

We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency and asymptotic normality of the estimator is established under a second order condition on the distribution underlying the data, and for intermediate sequences of upper order statistics. The finite sample properties of the proposed estimator and some alternatives from the extreme value literature are evaluated by a small simulation experiment involving both uncontaminated and contaminated samples.