On robust tail index estimation

A new approach to tail index estimation based on huberization of the Pareto MLE is considered. The proposed estimator is robust in a nonstandard way in that it protects against deviations from the central model at low quantiles. Asymptotic normality with the parametric n-rate of convergence is obtained with a bounded asymptotic bias under deviations from the Pareto model. The method is particularly useful for small samples where Hill-type estimators tend to be highly volatile. This is illustrated by a simulation study with sample sizes n≤100.