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Journal Articles Statistics and Computing Year : 2023

Estimation of extreme quantiles from heavy-tailed distributions with neural networks

Abstract

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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hal-03751980 , version 1 (16-08-2022)

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Michaël Allouche, Stéphane Girard, Emmanuel Gobet. Estimation of extreme quantiles from heavy-tailed distributions with neural networks. Statistics and Computing, 2023, 34 (12), pp.1-35. ⟨hal-03751980⟩
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