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.

中文翻译：

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一般尾一阶条件下极端条件分位数的估计

我们考虑极端条件分位数的估计。在第一部分中，我们提出了一个新的尾部条件，以建立一个极端条件分位数估计量的渐近分布。接下来，介绍了一类通用的估计器，其中包括核或最近邻类型的估计器。在新的尾部条件下提供了此类一般估计量的渐近正态性的统一定理，并在不同的知名示例中进行了说明。在小型模拟研究中提供了属于此类的不同估计器之间的比较，并在地震震级的真实数据集上进行了说明。