The study of estimation of conditional extreme
quantile in incomplete data frameworks is of growing interest. Specially, the
estimation of the extreme value index in a censorship framework has been the
purpose of many investigations when finite
dimension covariate information has been considered. In this paper, the
estimation of the conditional extreme quantile of a heavy-tailed
distribution is discussed when some functional random covariate (i.e. valued in some infinite-dimensional
space) information is available and the scalar response variable is
right-censored. A Weissman-type estimator of conditional extreme quantiles is
proposed and its asymptotic normality is established under mild assumptions. A
simulation study is conducted to assess the finite-sample behavior of the
proposed estimator and a comparison with two simple estimations strategies is
provided.
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