NeuralNetwork-Quantile-Extrapolation
Résumé
We propose new parametrizations for neural networks in order to estimate extreme
quantiles in both non-conditional and conditional heavy-tailed settings. All proposed
neural network estimators feature a bias correction based on an extension of the usual
second-order condition to an arbitrary order. The convergence rate of the uniform error
between extreme log-quantiles and their neural network approximation is established. The
finite sample performances of the non-conditional neural network estimator are compared
to other bias-reduced extreme-value competitors on simulated data. It is shown that
our method outperforms them in difficult heavy-tailed situations where other estimators
almost all fail. The source code is available at https://github.com/michael-allouche/
nn-quantile-extrapolation.git. Finally, the conditional neural network estimators
are implemented to investigate the behavior of extreme rainfalls as functions of their
geographical location in the southern part of France.
