Extreme value statistics for censored data with heavy tails under competing risks

In general, the interest lies in obtaining informations about the central characteristics of the underlying lifetime distribution (mean lifetime or survival probabilities for instance), often with the objective of comparing results between different conditions under which the lifetime data are acquired. In this work, we will address the problem of inferring about the (upper) tail of the lifetime distribution, for data subject both to random (right) censoring and competing risks. Suppose indeed that we are interested in the lifetimes of n individuals or items, which are subject to K different causes of death or failure, and to random censorship (from the right) as well. We are particularly interested in one of these causes (this main cause will be considered as cause number k thereafter, where k P t1,..., Ku), and we suppose that all causes are exclusive and are likely to be dependent on the others. The censoring time is assumed to be independent of the different causes of death or failure and of the observed lifetime itself.