Building nonstationary extreme value model using L-moments

2025-05-15

Journal of the Korean Statistical Society

AI Summary

Traditional maximum likelihood estimation for nonstationary extreme value modeling is sensitive to tail outliers, while L-moment methods suffer from performance degradation under positive variance trends. To address these issues, this paper proposes a robust nonstationary extreme value model. Methodologically, it integrates L-moment estimation with robust regression, employs standardized residuals to characterize covariate dependence of location and scale parameters, and introduces a novel generalized L-moment distance criterion—based on cross-validation—for model selection. Simulation studies demonstrate that the proposed method significantly improves parameter estimation accuracy under increasing-variance scenarios. When applied to peak flood flow data from Trehafod, UK, it enhances the robustness and reliability of return level estimation. Key contributions include: (i) the first L-moment framework explicitly designed to ensure both robustness and nonstationarity; (ii) a generalizable, cross-validated model selection criterion; and (iii) advancement of physically motivated, covariate-driven extreme event modeling.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Overcoming sensitivity of maximum likelihood in nonstationary extreme value models
• Improving L-moment methods for data with positive variance trends
• Developing robust parameter estimation using L-moments and regression

Innovation

• Uses L-moments for robust extreme value modeling
• Combines L-moments with standardized residual regression
• Extends method to covariate-based nonstationary models