final_program_abstracts[1]

11 IMSC Session Program
Regression quantiles methodology for choosing the optimal
threshold of the ‘peak- over- threshold’ method in climate
change simulations
Friday - Parallel Session 7
Jan Picek 1 , Martin Schindler 1 and Jan Kyselý 2
1 Technical University, Liberec, Czech Republic
2 Institute of Atmospheric Physics, Prague, Czech Republic
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.
The study is supported by the Czech Science Foundation under project P209/10/2045.
Abstracts 338