  This paper addresses the problem of estimating, in the presence of random
censoring as well as competing risks, the extreme value index of the
(sub)-distribution function associated to one particular cause, in the
heavy-tail case. Asymptotic normality of the proposed estimator (which has the
form of an Aalen-Johansen integral, and is the first estimator proposed in this
context) is established. A small simulation study exhibits its performances for
finite samples. Estimation of extreme quantiles of the cumulative incidence
function is also addressed.
