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Communication Dans Un Congrès Année : 2023

On the estimation of extreme quantiles with neural networks

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 behaviour of extreme rainfalls as functions of their geographical location in the southern part of France.
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Dates et versions

hal-04124085 , version 1 (09-06-2023)

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  • HAL Id : hal-04124085 , version 1

Citer

Michaël Allouche, Stéphane Girard, Emmanuel Gobet. On the estimation of extreme quantiles with neural networks. Journée "Evénements extrêmes et risques", réseau RESSTE (Risques, Extrêmes et Statistique Spatio-TEmporelle), Jun 2023, Marseille, France. ⟨hal-04124085⟩
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