Non-parametric extreme quantile estimation for the common shaped tail model

Abstract

The estimation of extreme quantile curves of a family of conditional distributions is a non-trivial problem, due to the data-sparseness in the tail of the distribution. This thesis considers the problem of post-processing extreme precipitation forecasts in Friesland from the numerical weather prediction model HARMONIE. Assuming forecasts are accurate, it is natural to assume a linear relationship between the precipitation observations and the forecasts. However, in practice this relationship is not linear, due to large uncertainties in the modelling process. To deal with this problem of non-linearity a non-parametric common shaped tail estimator (CST) is proposed to adequately estimate the non-linear shape of the relationship. Performance of the CST estimator is shown and compared to other extreme quantile estimators from the literature in an extensive simulation study. The estimators are also compared using the quantile verification skill score on a three year precipitation dataset in the province of Friesland. It is shown that the estimator has a lot of bias in the estimation, which prevents the CST estimator to outperform all other methods. However, the verification scores for the real data example exceed all scores of the other estimators.