Tail index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses

We are interested in the derivation of the distributional properties of a weighted log-excesses estimator of a positive tail index gamma. One of the main objectives of such an estimator is the accommodation of the dominant component of asymptotic bias, together with the maintenance of the asymptotic variance of the maximum likelihood estimator of gamma, under a strict Pareto model. We consider the external estimation not only of a second-order shape parameter rho but also of a second-order scale parameter beta. This will enable us to reduce the asymptotic variance of the final estimators under consideration, compared with second-order reduced bias estimators that are already available in the literature. The second-order reduced bias estimators that are considered are also studied for finite samples, through Monte Carlo techniques, as well as applied to real data in the field of finance.