Nonparametric estimation of the conditional tail index and extreme quantiles under random censoring

The estimation of the tail index and extreme quantiles of a heavy-tailed distribution is addressed when some covariate information is available and the data are randomly right-censored. Several estimators are constructed by combining a moving-window technique (for tackling the covariate information) and the inverse probability-of-censoring weighting method. The asymptotic normality of these estimators is established and their finite-sample properties are investigated via simulations. A comparison with alternative estimators is provided. Finally, the proposed methodology is illustrated on a medical dataset.