  On the basis of Nelson-Aalen nonparametric estimator of the cumulative
distribution function, we provide a weak approximation to tail product-limit
process for randomly right-censored heavy-tailed data. In this context, a new
consistent reduced-bias estimator of the extreme value index is introduced and
its asymptotic normality is established only by assuming the second-order
regular variation of the underlying distribution function. A simulation study
shows that the newly proposed estimator performs better than the existing ones.
