Fast parameter estimation of Generalized Extreme Value distribution
  using Neural Networks
Sweta Rai Alexis Hoffman Soumendra Lahiri Douglas W. Nychka Stephan R. Sain Soutir Bandyopadhyay
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.