Nelson-Aalen tail product-limit process and extreme value index estimation under random censorship

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.