Before revision:  Since these distributions are not pivotal, we also introduce a novel trimmed wild bootstrap procedure, which does not require additional nonparametric smoothing , typically needed in such settings, and show its consistency. We find in Monte Carlo experiments  that shape restrictions can improve dramatically the finite-sample performance of unrestricted estimators.
After revision:  Since these distributions are not pivotal, we also introduce a novel trimmed wild bootstrap procedure, which does not require additional nonparametric smoothing which is not the case for the interior point. The Monte Carlo experiments that shape restrictions can improve dramatically the finite-sample performance of unrestricted estimators.