The widely used statistical methods of the extreme value analysis, based on either 'block maxima' or 'peaks-over-threshold' representation of extremes, assume stationarity of extreme values. Such assumption is often violated due to existing trends or long-term variability in the investigated series. This is also the case for climate model simulations carried out under variable external forcings, originating e.g. from increasing greenhouse gas concentrations in the atmosphere. Applying the POT approach involves the selection of an appropriate covariate-dependent threshold. Koenker and Basset in 1978 introduced regression quantiles as a generalization of usual quantiles to a linear regression model. The key idea in generalizing the quantiles is that one can express the problem of finding the sample quantile as the solution to a simple optimization problem. The covariate-dependent threshold set as a particular regression quantile yields exceedances over the whole range of years whereas for a constant threshold, exceedances occur more frequently (or almost exclusively) in later years, which violates assumptions of the extreme value analysis. Several variants of the regression quantiles are compared; the choice of the order is based on the quantile likelihood ratio test and the rank test based on regression rank scores.
Keywords: Regression quantile; Peak-over-threshold method; Extreme
Biography: Associate professor at Technical University of Liberec.
Coauthor Robust Statistical Methods with R, Chapman & Hall/CRC. Boca Raton 2005.