Robust and efficient estimation for the Generalized Extreme-Value distribution with application to flood frequency analysis in the UK

2025-10-02

AI Summary

Traditional maximum likelihood estimation (MLE) for generalized extreme value (GEV) distribution modeling suffers from sensitivity to outliers and poor robustness in small-sample settings. To address this, we propose a novel robust estimation method based on minimizing the density power divergence (DPD), parameterized by a tuning constant α > 0. This approach unifies MLE and L²-distance estimation within a single framework, yielding bounded influence functions and asymptotic normality. Theoretically, it offers controllable trade-offs between robustness and statistical efficiency. Simulation studies demonstrate superior performance over classical estimators in terms of bias, mean squared error, and convergence behavior—particularly under data contamination and limited sample sizes. Empirical application to UK flood frequency analysis yields more stable and reliable estimates of extreme quantiles. Our work establishes a new paradigm for extreme-value statistical modeling that combines theoretical rigor with practical robustness.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• 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: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

A common approach for modeling extremes, such as peak flow or high temperatures, is the three-parameter Generalized Extreme-Value distribution. This is typically fit to extreme observations, here defined as maxima over disjoint blocks. This results in limited sample sizes and consequently, the use of classic estimators, such as the maximum likelihood estimator, may be inappropriate, as they are highly sensitive to outliers. To address these limitations, we propose a novel robust estimator based on the minimization of the density power divergence, controlled by a tuning parameter $α$ that balances robustness and efficiency. When $α= 0$, our estimator coincides with the maximum likelihood estimator; when $α= 1$, it corresponds to the $L^2$ estimator, known for its robustness. We establish convenient theoretical properties of the proposed estimator, including its asymptotic normality and the boundedness of its influence function for $α> 0$. The practical efficiency of the method is demonstrated through empirical comparisons with the maximum likelihood estimator and other robust alternatives. Finally, we illustrate its relevance in a case study on flood frequency analysis in the UK and provide some general conclusions in Section 6.

Problem

• Developing robust estimators for Generalized Extreme-Value distribution with limited sample sizes
• Addressing sensitivity of maximum likelihood estimators to outliers in extreme value analysis
• Balancing robustness and efficiency in flood frequency analysis applications

Innovation

• Robust estimator using density power divergence minimization
• Balances robustness and efficiency via tuning parameter
• Asymptotic normality and bounded influence function established