  The notion of expectiles, originally introduced in the context of testing for
homoscedasticity and conditional symmetry of the error distribution in linear
regression, induces a law-invariant, coherent and elicitable risk measure that
has received a significant amount of attention in actuarial and financial risk
management contexts. A number of recent papers have focused on the behaviour
and estimation of extreme expectile-based risk measures and their potential for
risk management. Joint inference of several extreme expectiles has however been
left untouched; in fact, even the inference of a marginal extreme expectile
turns out to be a difficult problem in finite samples. We investigate the
simultaneous estimation of several extreme marginal expectiles of a random
vector with heavy-tailed marginal distributions. This is done in a general
extremal dependence model where the emphasis is on pairwise dependence between
the margins. We use our results to derive accurate confidence regions for
extreme expectiles, as well as a test for the equality of several extreme
expectiles. Our methods are showcased in a finite-sample simulation study and
on real financial data.
