Bias-reduced estimators of the Weibull tail-coefficient

In this paper, we consider the problem of the estimation of the Weibull tail-coefficient θ. In particular, we propose a regression model, from which we derive a bias-reduced estimator of θ. This estimator is based on a least-squares approach. The asymptotic normality of this estimator is established. We also introduce an adaptive selection procedure to determine the number of upper order statistics to be used in the estimator. A simulation study as well as an application to a real data set are provided in order to prove the efficiency of the above mentioned methods.