Estimating the conditional extreme-value index under random right-censoring
Résumé
In extreme value theory, the extreme-value index is a parameter that controls the behavior of a cumulative distribution function in its right tail. Estimating this parameter is thus the first step when tackling a number of problems related to extreme events. In this paper, we introduce an estimator of the extreme-value index in the presence of a random covariate when the response variable is right-censored, whether its conditional distribution belongs to the Fréchet, Weibull or Gumbel max-domain of attraction. The pointwise weak consistency and asymptotic normality of the proposed estimator are established. Some illustrations on simulations are provided and we showcase the estimator on a real set of medical data.
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