Estimation of the conditional extreme-value index and extreme quantiles with random covariates and censoring

Résumé

In this talk, estimation of the extreme-value index of a heavy-tailed distribution is addressed when some random covariate information is available and the data are randomly right-censored. An inverse-probability-of-censoring-weighted kernel version of Hill's estimator of the extreme value index is proposed and its asymptotic normality is established. Based on this, a Weissman-type estimator of conditional extreme quantiles is constructed. A simulation study is conducted to assess the finite-sample behaviour of the proposed estimators. The methodology is illustrated on a real data set.