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, etc. 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 (GEV) 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 (CCSM3) across North America for three atmospheric concentrations: 289 ppm $\mathrm{CO}_2$ (pre-industrial), 700 ppm $\mathrm{CO}_2$ (future conditions), and 1400 ppm $\mathrm{CO}_2$, and compare the results with those obtained using the maximum likelihood approach.

翻译：重尾特性使广义极值分布成为建模洪水、干旱、热浪、野火等极端事件的热门选择。然而，即使对于中等规模数据集，使用传统最大似然方法估计该分布参数也可能面临计算密集型问题。为克服这一局限，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能够以与常规最大似然法相当的精度提供广义极值分布参数估计，同时显著提升计算速度。为考虑估计不确定性，我们利用训练网络固有的参数自举法。最后，我们将该方法应用于北美地区社区气候系统模型第三版（CCSM3）中三种大气浓度（289 ppm $\mathrm{CO}_2$（工业化前）、700 ppm $\mathrm{CO}_2$（未来情景）和1400 ppm $\mathrm{CO}_2$）的1000年年度最高温度数据，并将结果与最大似然法进行比较。