Title: Building nonstationary extreme value model using L-moments Show Chinese title

Title: 利用 L-矩构建非平稳极值模型

Abstract: The maximum likelihood estimation for a time-dependent nonstationary (NS) extreme value model is often too sensitive to influential observations, such as large values toward the end of a sample. Thus, alternative methods using L-moments have been developed in NS models to address this problem while retaining the advantages of the stationary L-moment method. However, one method using L-moments displays inferior performance compared to stationary estimation when the data exhibit a positive trend in variance. To address this problem, we propose a new algorithm for efficiently estimating the NS parameters. The proposed method combines L-moments and robust regression, using standardized residuals. A simulation study demonstrates that the proposed method overcomes the mentioned problem. The comparison is conducted using conventional and redefined return level estimates. An application to peak streamflow data in Trehafod in the UK illustrates the usefulness of the proposed method. Additionally, we extend the proposed method to a NS extreme value model in which physical covariates are employed as predictors. Furthermore, we consider a model selection criterion based on the cross-validated generalized L-moment distance as an alternative to the likelihood-based criteria. Show Chinese abstract

Abstract: 对于一个时变非平稳（NS）极值模型，最大似然估计通常对有影响的观测值（如样本末尾的大值）过于敏感。因此，在非平稳模型中开发了使用L矩的替代方法来解决这个问题，同时保留了平稳L矩方法的优点。然而，当数据表现出方差的正趋势时，使用L矩的一种方法的表现不如平稳估计。为了解决这个问题，我们提出了一种新的算法，以有效地估计非平稳参数。所提出的方法结合了L矩和鲁棒回归，并使用标准化残差。模拟研究表明，所提出的方法克服了上述问题。比较基于常规和重新定义的回溯水平估计。对英国特雷霍福德河流峰值流量数据的应用展示了所提出方法的有用性。此外，我们将所提出的方法扩展到使用物理协变量作为预测因子的非平稳极值模型中。另外，我们考虑了一个基于交叉验证广义L矩距离的模型选择标准，作为基于似然函数标准的替代方案。