Several modifications of DPR estimator of the tail index

In this paper, we continue the investigation of an estimator proposed in Yu. Davydov, V. Paulauskas, and A. Račkauskas, More on p-stable convex sets in Banach spaces, J. Theor. Probab., 13:39–64, 2000] and V. Paulauskas, A new estimator for tail index, Acta Appl. Math., 79:55–67, 2003] and considered in V. Paulauskas and M. Vaičiulis, Once more on comparison of tail index estimators, preprint, 2010]. We propose a class of modifications of the so-called DPR estimator and demonstrate that these modifications can have better asymptotic properties than the original DPR estimator.