Print Email Facebook Twitter Gradient boosting for extreme quantile regression Title Gradient boosting for extreme quantile regression Author Velthoen, J.J. (TU Delft Statistics) Dombry, Clément (Université de Bourgogne) Cai, Juan Juan (Vrije Universiteit Amsterdam) Engelke, Sebastian (Université de Genève) Date 2023 Abstract Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used for extrapolation beyond the range of observed values and estimation of conditional extreme quantiles. Based on the peaks-over-threshold approach, the conditional distribution above a high threshold is approximated by a generalized Pareto distribution with covariate dependent parameters. We propose a gradient boosting procedure to estimate a conditional generalized Pareto distribution by minimizing its deviance. Cross-validation is used for the choice of tuning parameters such as the number of trees and the tree depths. We discuss diagnostic plots such as variable importance and partial dependence plots, which help to interpret the fitted models. In simulation studies we show that our gradient boosting procedure outperforms classical methods from quantile regression and extreme value theory, especially for high-dimensional predictor spaces and complex parameter response surfaces. An application to statistical post-processing of weather forecasts with precipitation data in the Netherlands is proposed. Subject 60G7062G08Extreme quantile regressionExtreme value theoryGeneralized Pareto distributionGradient boostingTree-based methods To reference this document use: http://resolver.tudelft.nl/uuid:5834a75d-b3ab-4120-8153-b31188b7fd34 DOI https://doi.org/10.1007/s10687-023-00473-x ISSN 1386-1999 Source Extremes: statistical theory and applications in science, engineering and economics, 26 (4), 639-667 Part of collection Institutional Repository Document type journal article Rights © 2023 J.J. Velthoen, Clément Dombry, Juan Juan Cai, Sebastian Engelke Files PDF s10687_023_00473_x.pdf 5.08 MB Close viewer /islandora/object/uuid:5834a75d-b3ab-4120-8153-b31188b7fd34/datastream/OBJ/view