  Marginal expected shortfall is unquestionably one of the most popular
systemic risk measures. Studying its extreme behaviour is particularly relevant
for risk protection against severe global financial market downturns. In this
context, results of statistical inference rely on the bivariate extreme values
approach, disregarding the extremal dependence among a large number of
financial institutions that make up the market. In order to take it into
account we propose an inferential procedure based on the multivariate regular
variation theory. We derive an approximating formula for the extreme marginal
expected shortfall and obtain from it an estimator and its bias-corrected
version. Then, we show their asymptotic normality, which allows in turn the
confidence intervals derivation. Simulations show that the new estimators
greatly improve upon the performance of existing ones and confidence intervals
are very accurate. An application to financial returns shows the utility of the
proposed inferential procedure. Statistical results are extended to a general
$\beta$-mixing context that allows to work with popular time series models with
heavy-tailed innovations.
