arXiv 2510.033382025-10-02stat.APmath.STstat.MEstat.TH

广义极值分布的稳健高效估计及其在英国洪水频率分析中的应用

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

Nathan Huet, Ilaria Prosdocimi

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AI总结：

针对区块极值样本有限且最大似然估计易受异常值影响的问题，提出基于密度幂散度、由 α 调节稳健性与效率的广义极值分布估计量，并验证其理论性质、实证表现及英国洪水频率分析应用。

摘要：

对极值（如洪峰流量或高温）进行建模的一种常用方法是三参数广义极值分布。该分布通常拟合于极值观测值，本文将其定义为互不相交区块上的最大值。这会导致样本量有限，因此使用最大似然估计量等经典估计量可能并不合适，因为它们对异常值高度敏感。为克服这些局限，我们提出一种新型稳健估计量，其基础是最小化密度幂散度，并由调谐参数 α 控制，以平衡稳健性与效率。当 α=0 时，我们的估计量与最大似然估计量一致；当 α=1 时，它对应于以稳健性著称的 L² 估计量。我们建立了所提估计量的便利理论性质，包括其渐近正态性以及在 α>0 时影响函数的有界性。通过与最大似然估计量及其他稳健替代方法进行实证比较，证明了该方法的实际效率。最后，我们在英国洪水频率分析案例研究中说明其相关性，并在第6节给出若干一般性结论。

英文摘要：

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.

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