We introduce and study Multi-Quantile estimators for the parameters $( \xi, \sigma, \mu)$ of Generalized Extreme Value (GEV) distributions to provide a robust approach to extreme value modeling. Unlike classical estimators, such as the Maximum Likelihood Estimation (MLE) estimator and the Probability Weighted Moments (PWM) estimator, which impose strict constraints on the shape parameter $\xi$, our estimators are always asymptotically normal and consistent across all values of the GEV parameters. The asymptotic variances of our estimators decrease with the number of quantiles increasing and can approach the Cram\'er-Rao lower bound very closely whenever it exists. Our Multi-Quantile Estimators thus offer a more flexible and efficient alternative for practical applications. We also discuss how they can be implemented in the context of Block Maxima method.

翻译：本文提出并研究了广义极值分布参数$( \xi, \sigma, \mu)$的多分位数估计方法，为极值建模提供了一种稳健的估计途径。与经典的最大似然估计和概率加权矩估计等方法不同——这些方法对形状参数$\xi$施加了严格的限制——我们的估计量在所有广义极值分布参数取值下均保持渐近正态性和一致性。估计量的渐近方差随着所采用分位数数量的增加而减小，且当克拉默-拉奥下界存在时，该方差可无限逼近该下界。因此，多分位数估计方法为实际应用提供了更为灵活且高效的替代方案。本文亦探讨了该方法在区块最大值框架下的具体实现。