Nonparametric estimation of the conditional extreme-value index with random covariates and censoring

• We estimate extreme value index and extreme quantiles of a heavy-tailed distribution with covariates and censoring.
• We prove asymptotic normality of our estimator of the conditional extreme value index.
• We assess the finite-sample behavior of the proposed estimators via simulations.

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. A 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 behavior of the proposed estimators.