Generalized method of L-moment estimation for stationary and nonstationary extreme value models

2025-12-23

AI Summary

To address the substantial bias and poor robustness of parameter estimation for the Generalized Extreme Value (GEV) distribution under small-sample conditions, this paper proposes a novel Generalized L-moment Estimation (GLME) framework. We first formulate GLME by incorporating penalty functions or prior information; design two data-adaptive penalty terms to correct L-moment estimation bias; and unify the framework within both penalized likelihood and Bayesian paradigms by integrating the L-moment distance with a multivariate normal likelihood approximation—enabling seamless extension to both stationary and non-stationary GEV modeling. Monte Carlo simulations and empirical applications to U.S. flood loss and Thai rainfall extremes demonstrate that GLME significantly reduces parameter estimation bias and markedly improves accuracy in upper-quantile risk assessment, while incurring only a marginal increase in standard errors.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Precisely estimating out-of-sample upper quantiles is very important in risk assessment and in engineering practice for structural design to prevent a greater disaster. For this purpose, the generalized extreme value (GEV) distribution has been broadly used. To estimate the parameters of GEV distribution, the maximum likelihood estimation (MLE) and L-moment estimation (LME) methods have been primarily employed. For a better estimation using the MLE, several studies considered the generalized MLE (penalized likelihood or Bayesian) methods to cooperate with a penalty function or prior information for parameters. However, a generalized LME method for the same purpose has not been developed yet in the literature. We thus propose the generalized method of L-moment estimation (GLME) to cooperate with a penalty function or prior information. The proposed estimation is based on the generalized L-moment distance and a multivariate normal likelihood approximation. Because the L-moment estimator is more efficient and robust for small samples than the MLE, we reasonably expect the advantages of LME to continue to hold for GLME. The proposed method is applied to the stationary and nonstationary GEV models with two novel (data-adaptive) penalty functions to correct the bias of LME. A simulation study indicates that the biases of LME are considerably corrected by the GLME with slight increases in the standard error. Applications to US flood damage data and maximum rainfall at Phliu Agromet in Thailand illustrate the usefulness of the proposed method. This study may promote further work on penalized or Bayesian inferences based on L-moments.

Problem

• Develops a generalized L-moment estimation method for extreme value models.
• Incorporates penalty functions or prior information to correct estimation bias.
• Applies the method to stationary and nonstationary GEV models for risk assessment.

Innovation

• Generalized L-moment estimation with penalty functions
• Multivariate normal likelihood approximation for bias correction
• Application to stationary and nonstationary extreme value models