  We revisit the model of heteroscedastic extremes initially introduced by
Einmahl et al. (JRSSB, 2016) to describe the evolution of a non stationary
sequence whose extremes evolve over time and adapt it into a general extreme
quantile regression framework. We provide estimates for the extreme value index
and the integrated skedasis function and prove their asymptotic normality. Our
results are quite similar to those developed for heteroscedastic extremes but
with a different proof approach emphasizing coupling arguments. We also propose
a pointwise estimator of the skedasis function and a Weissman estimator of the
conditional extreme quantile and prove the asymptotic normality of both
estimators.
