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We consider the estimation of an extreme conditional quantile. In a first part, we propose a new tail condition in order to establish the asymptotic distribution of an extreme conditional quantile estimator. Next, a general class of estimators is introduced, which encompasses, among others, kernel or nearest neighbors types of estimators. A unified theorem of the asymptotic normality for this general class of estimators is provided under the new tail condition and illustrated on the different well-known examples. A comparison between different estimators belonging to this class is provided on a small simulation study and illustrated on a real dataset on earthquake magnitudes. [ABSTRACT FROM AUTHOR]

We consider the estimation of the tail coefficient of a Weibull-type distribution in the presence of random covariates. The approach followed is non-parametric and consists of locally weighted estimation in narrow neighbourhoods in the covariate space. We introduce two families of estimators and study their asymptotic behaviour under some conditions on the conditional response distribution, the kernel function, the density function of the independent variables, and for appropriately chosen bandwidth and threshold parameters. We also introduce a Weissman-type estimator for estimating upper extreme conditional quantiles. The finite sample behaviour of the proposed estimators is examined with a simulation experiment. The practical applicability of the methodology is illustrated on a dataset of sea storm measurements. [ABSTRACT FROM AUTHOR]