Fast parameter estimation of generalized extreme value distribution using neural networks

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.