Asymptotic properties of generalized DPR statistic

We investigate asymptotic properties of the so-called generalized Davydov, Paulauskas, and Račkauskas statistic that was introduced in [V. Paulauskas and M. Vaičiulis, Several modifications of DPR estimator of the tail index, Lith. Math. J., 51(1):36–50, 2011]. We obtain an asymptotics of the bias of this statistic and show that this statistic is asymptotically normal. As an application, we provide a new class of semiparametric heavy-tailed estimators and compare these estimators with other estimators, including the popular Hill and Pickands estimators.