The heavy-tailed behavior of the generalized extreme-value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires and so forth. However, estimating the distribution's parameters using conventional maximum likelihood methods can be computationally intensive, even for moderate-sized datasets. To overcome this limitation, we propose a computationally efficient, likelihood-free estimation method utilizing a neural network. Through an extensive simulation study, we demonstrate that the proposed neural network-based method provides generalized extreme value distribution parameter estimates with comparable accuracy to the conventional maximum likelihood method but with a significant computational speedup. To account for estimation uncertainty, we utilize parametric bootstrapping, which is inherent in the trained network. Finally, we apply this method to 1000-year annual maximum temperature data from the Community Climate System Model version 3 across North America for three atmospheric concentrations: 289 ppm ${\text{CO}}_2$ (pre-industrial), 700 ppm ${\text{CO}}_2$ (future conditions), and 1400 ppm ${\text{CO}}_2$, and compare the results with those obtained using the maximum likelihood approach.

中文翻译：

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使用神经网络进行广义极值分布的快速参数估计

广义极值分布的重尾行为使其成为对洪水、干旱、热浪、野火等极端事件进行建模的流行选择。然而，使用传统的最大似然方法估计分布参数可能需要大量计算，即使对于中等大小的数据集也是如此。为了克服这一限制，我们提出了一种利用神经网络的计算高效、无似然估计方法。通过广泛的模拟研究，我们证明所提出的基于神经网络的方法提供了广义极值分布参数估计，其精度与传统的最大似然法相当，但计算速度显着加快。为了考虑估计的不确定性，我们利用参数自举，这是经过训练的网络所固有的。最后，我们将此方法应用于来自整个北美社区气候系统模型版本 3 的 1000 年年度最高温度数据，其中三种大气浓度为：289 ppm${\text{一氧化碳}}_2$（工业化前），700 ppm${\text{一氧化碳}}_2$（未来条件）和 1400 ppm${\text{一氧化碳}}_2$，并将结果与​​使用最大似然法获得的结果进行比较。