Spatial extreme quantile estimation using a weighted log-likelihood approach

Carreau, Julie; Girard, Stéphane

Journal de la société française de statistique, Tome 152 (2011) no. 3, pp. 66-82.

Nous proposons d’estimer des quantiles extrêmes spatiaux par une approche de type log-vraisemblance pondérée. Pour cela, nous supposons que, conditionnellement aux covariables, la variable d’intérêt suit une loi des valeurs extrêmes. Les surfaces de réponse associées sont estimées en introduisant des poids dans la log-vraisemblance. Ces poids dépendent de la distance entre le point d’estimation et les observations. La construction d’une distance appropriée repose sur la combinaison d’une étape de dépliage par “multidimensional scaling” et d’une étape de régression par réseaux de neurones. Notre approche est illustrée sur des jeux de données réelles et simulées.

We propose to estimate spatial extreme quantiles by a weighted log-likelihood approach. It is assumed that the conditional distribution of the variable of interest follows a generalized extreme-value distribution. The associated response surfaces are estimated thanks to the introduction of weights in the log-likelihood. These weights depend on the distance between the point of interest and the observations. The construction of a proper distance relies on the combination of a multidimensional scaling unfolding with a neural network regression. Our approach is illustrated both on simulated and real rainfall datasets.

Mots clés : generalized extreme-value distribution, semi-parametric estimation, multidimensional scaling, neural networks

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