On the study of extremes with dependent random right-censoring
Résumé
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. In this paper, we look instead at the dependent
case. More precisely, we consider the case when the structure of the dependent censoring mechanism
is given by an extreme value copula. In this context, we examine the extremes of the response variable
(that is, the minimum between time-to-event and time-to-censoring) and of the probability of
censoring in the right tail of this variable. We then draw a number of consequences of our results,
related to the asymptotic behaviour, in this dependent context, 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.
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