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.
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.
@article{JSFS_2011__152_3_66_0, author = {Carreau, Julie and Girard, St\'ephane}, title = {Spatial extreme quantile estimation using a weighted log-likelihood approach}, journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique}, pages = {66--82}, publisher = {Soci\'et\'e fran\c{c}aise de statistique}, volume = {152}, number = {3}, year = {2011}, mrnumber = {2871177}, zbl = {1316.62062}, language = {en}, url = {http://archive.numdam.org/item/JSFS_2011__152_3_66_0/} }
TY - JOUR AU - Carreau, Julie AU - Girard, Stéphane TI - Spatial extreme quantile estimation using a weighted log-likelihood approach JO - Journal de la société française de statistique PY - 2011 SP - 66 EP - 82 VL - 152 IS - 3 PB - Société française de statistique UR - http://archive.numdam.org/item/JSFS_2011__152_3_66_0/ LA - en ID - JSFS_2011__152_3_66_0 ER -
%0 Journal Article %A Carreau, Julie %A Girard, Stéphane %T Spatial extreme quantile estimation using a weighted log-likelihood approach %J Journal de la société française de statistique %D 2011 %P 66-82 %V 152 %N 3 %I Société française de statistique %U http://archive.numdam.org/item/JSFS_2011__152_3_66_0/ %G en %F JSFS_2011__152_3_66_0
Carreau, Julie; Girard, Stéphane. Spatial extreme quantile estimation using a weighted log-likelihood approach. Journal de la société française de statistique, Volume 152 (2011) no. 3, pp. 66-82. http://archive.numdam.org/item/JSFS_2011__152_3_66_0/
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