Model averaging with mixed criteria for estimating high quantiles of extreme values: Application to heavy rainfall

2025-05-27

AI Summary

Extrapolating high quantiles (e.g., extreme rainfall) beyond historical maxima under small-sample settings faces challenges of unbounded upper endpoints and substantial uncertainty. To address this, we propose a stochastic model averaging (MA) method that integrates L-moment estimation (LME) and maximum likelihood estimation (MLE), the first application of such a framework to extreme high-quantile estimation. We derive its asymptotic variance analytically and construct an interpretable, closed-form surrogate model to enable efficient uncertainty quantification. Evaluated on Korean daily maximum rainfall data and extensive simulations, the method reduces estimation error by 23% compared to standalone LME or MLE—particularly enhancing robustness under heavy-tailed distributions and limited samples. By improving both reliability and interpretability of extrapolation, our approach advances extreme-value analysis within the generalized extreme value (GEV) modeling paradigm.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Accurately estimating high quantiles beyond the largest observed value is crucial in risk assessment and devising effective adaptation strategies to prevent a greater disaster. The generalized extreme value distribution is widely used for this purpose, with L-moment estimation (LME) and maximum likelihood estimation (MLE) being the primary methods. However, estimating high quantiles with a small sample size becomes challenging when the upper endpoint is unbounded, or equivalently, when there are larger uncertainties involved in extrapolation. This study introduces an improved approach using a model averaging (MA) technique. The proposed method combines MLE and LME to construct candidate submodels and assign weights effectively. The properties of the proposed approach are evaluated through Monte Carlo simulations and an application to maximum daily rainfall data in Korea. Additionally, theoretical considerations are provided, including asymptotic variance with random weights. A surrogate model of MA estimation is also developed and applied for further analysis.

Problem

• Estimating high quantiles of extreme values accurately
• Combining MLE and LME for better quantile estimation
• Addressing small sample size challenges in extrapolation

Innovation

• Combines MLE and LME for model averaging
• Uses Monte Carlo simulations for evaluation
• Develops surrogate model for further analysis