  In this paper, we investigate the problem of nonparametric monotone frontier
estimation from the perspective of extreme value theory. This enables us to
revisit the asymptotic theory of the popular free disposal hull estimator in a
more general setting, to derive new and asymptotically Gaussian estimators and
to provide useful asymptotic confidence bands for the monotone boundary
function. The finite-sample behavior of the suggested estimators is explored
via Monte Carlo experiments. We also apply our approach to a real data set
based on the production activity of the French postal services.
