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, 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 examine the extremes of the response variable (that is, the minimum between time-to-event and time-to-censoring) and the probability of censoring in the right tail of this variable when the structure of the dependent censoring mechanism is given by an extreme value copula. Statistically speaking, our results have important consequences on the identifiability problem for the extremes of the variable of interest: most strikingly, and in contrast to the independent censoring case, if the censoring variable has a lighter tail than the variable of interest and the dependence structure is given by a non-independent extreme value copula, then the extremes of the variable of interest appear to be unrecoverable.
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