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.

[1]  M. C. Jones,et al.  Local Linear Quantile Regression , 1998 .

[2]  S. Girard,et al.  On kernel smoothing for extremal quantile regression , 2012, 1312.5123.

[3]  Stéphane Girard,et al.  Functional nonparametric estimation of conditional extreme quantiles , 2010, J. Multivar. Anal..

[4]  A. Rényi.  On the theory of order statistics , 1953 .

[5]  A. Guillou,et al.  A local moment type estimator for the extreme value index in regression with random covariates , 2014 .

[6]  R. Koenker.  Quantile Regression: Name Index , 2005 .

[7]  Yingcun Xia,et al.  UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL , 2007, Econometric Theory.

[8]  L. Gardes,et al.  An integrated functional Weissman estimator for conditional extreme quantiles , 2017 .

[9]  Richard L. Smith,et al.  Models for exceedances over high thresholds , 1990 .

[10]  Deyuan Li,et al.  Estimation of Extreme Conditional Quantiles Through Power Transformation , 2013 .

[11]  Victor Chernozhukov,et al.  Quantile regression , 2019, Journal of Econometrics.

[12]  Petra Friederichs,et al.  Decomposition and graphical portrayal of the quantile score , 2014 .

[13]  C. Zhou,et al.  On spatial extremes: With application to a rainfall problem , 2008, 0807.4092.

[14]  Eugenia Kalnay,et al.  Atmospheric Modeling, Data Assimilation and Predictability , 2002 .

[15]  Jonathan A. Tawn,et al.  Modelling extremes of the areal rainfall process. , 1996 .

[16]  A local moment type estimator for an extreme quantile in regression with random covariates , 2017 .

[17]  P. Friederichs,et al.  Generating and Calibrating Probabilistic Quantitative Precipitation Forecasts from the High-Resolution NWP Model COSMO-DE , 2012 .

[18]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[19]  S. Girard,et al.  Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels , 2010 .

[20]  Deyuan Li,et al.  Estimation of High Conditional Quantiles for Heavy-Tailed Distributions , 2012 .

[21]  Jan Beirlant,et al.  Nonparametric estimation of extreme conditional quantiles , 2004 .

[22]  S. Girard,et al.  Kernel estimators of extreme level curves , 2011 .

[23]  W. Briggs.  Statistical Methods in the Atmospheric Sciences , 2007 .

[24]  Carlos Martins-Filho,et al.  NONPARAMETRIC ESTIMATION OF CONDITIONAL VALUE-AT-RISK AND EXPECTED SHORTFALL BASED ON EXTREME VALUE THEORY , 2016, Econometric Theory.