Abstract
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.
Highlights
Extreme precipitation events can cause large economic losses, when large amounts of water cannot be properly drained
Weather forecasting relies on deterministic forecasts obtained by numerical weather prediction (NWP) models (Kalnay 2003)
A local approach, where an extreme quantile estimator is applied to a sequence of estimated quantiles for moderately high probability levels attained from the first step
Summary
Extreme precipitation events can cause large economic losses, when large amounts of water cannot be properly drained. A local approach, where an extreme quantile estimator is applied to a sequence of estimated quantiles for moderately high probability levels attained from the first step This method is used in (Wang et al 2012; Wang and Li 2013; Daouia et al 2011; Daouia et al 2013; Gardes et al 2010; Goegebeur et al 2014) and Gardes and Stupfler (2019). An application of the result of Davison and Smith (1990) to precipitation data is discussed in Bentzien and Friederichs (2012), where a generalized Pareto distribution is fitted to the exceedances above an estimated linear quantile. They showed skilful short-range forecasts of extreme quantiles. The proofs of the theoretical results are provided in the appendix
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