On the study of extremes with dependent random right-censoring

The study of extremes in missing data frameworks is a recent developing field. In particular, the randomly right-censored case has been receiving a fair amount of attention in the last decade. All studies on this topic, however, essentially work under the usual assumption that the variable of interest and the censoring variable are independent. Furthermore, a frequent characteristic of estimation procedures developed so far is their crucial reliance on particular properties of the asymptotic behaviour of the response variable Z (that is, the minimum between time-to-event and time-to-censoring) and of the probability of censoring in the right tail of Z. In this paper, we focus instead on elucidating this asymptotic behaviour in the dependent censoring case, and, more precisely, when the structure of the dependent censoring mechanism is given by an extreme value copula. We then draw a number of consequences of our results, related to the asymptotic behaviour, in this dependent context, of a number of estimators of the extreme value index of the random variable of interest that were introduced in the literature under the assumption of independent censoring, and we discuss more generally the implications of our results on the inference of the extremes of this variable.