arXiv subjects

Jasper Velthoen

Publications and source records attributed to Jasper Velthoen.

3 recordsLinked to original sources

arXiv2021

Gradient boosting for extreme quantile regression

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.

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arXiv2020

Interpretable random forest models through forward variable selection

Random forest is a popular prediction approach for handling high dimensional covariates. However, it often becomes infeasible to interpret the obtained high dimensional and non-parametric model. Aiming for obtaining an interpretable predictive model, we develop a forward variable selection method using the continuous ranked probability score (CRPS) as the loss function. Our stepwise procedure leads to a smallest set of variables that optimizes the CRPS risk by performing at each step a hypothesis test on a significant decrease in CRPS risk. We provide mathematical motivation for our method by proving that in population sense the method attains the optimal set. Additionally, we show that the test is consistent provided that the random forest estimator of a quantile function is consistent. In a simulation study, we compare the performance of our method with an existing variable selection method, for different sample sizes and different correlation strength of covariates. Our method is observed to have a much lower false positive rate. We also demonstrate an application of our method to statistical post-processing of daily maximum temperature forecasts in the Netherlands. Our method selects about 10% covariates while retaining the same predictive power.

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arXiv2019

Improving precipitation forecasts using extreme quantile regression

Aiming to estimate extreme precipitation forecast quantiles, we propose a nonparametric regression model that features a constant extreme value index. Using local linear quantile regression and an extrapolation technique from extreme value theory, we develop an estimator for conditional quantiles corresponding to extreme high probability levels. We establish uniform consistency and asymptotic normality of the estimators. In a simulation study, we examine the performance of our estimator on finite samples in comparison with a method assuming linear quantiles. On a precipitation data set in the Netherlands, these estimators have greater predictive skill compared to the upper member of ensemble forecasts provided by a numerical weather prediction model.

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