  A tail empirical process for heavy-tailed and right-censored data is
introduced and its Gaussian approximation is established. In this context, a
(weighted) new Hill-type estimator for positive extreme value index is proposed
and its consistency and asymptotic normality are proved by means of the
aforementioned process in the framework of second-order conditions of regular
variation. In a comparative simulation study, the newly defined estimator is
seen to perform better than the already existing ones in terms of both bias and
mean squared error. As a real data example, we apply our estimation procedure
to evaluate the tail index of the survival time of Australian male Aids
patients. It is noteworthy that our approach may also serve to develop other
statistics related to the distribution tail such as second-order parameter and
reduced-bias tail index estimators. Furthermore, the proposed tail empirical
process provides a goodness-of-fit test for Pareto-like models under
censorship.
