Robust nonparametric estimators of monotone boundaries

This paper revisits some asymptotic properties of the robust nonparametric estimators of order-in and order-alpha quantile frontiers and proposes isotonized version of these estimators. Previous convergence properties of the order-in frontier are extended (from weak uniform convergence to complete uniform convergence). Complete uniform convergence of the order-in (and of the quantile order-alpha) nonparametric estimators to the boundary is also established, for an appropriate choice of in (and of a, respectively) as a function of the sample size. The new isotonized estimators share the asymptotic Aa properties of the original ones and a simulated example shows, as expected, that these new versions are even more robust than the original estimators. The procedure is also illustrated through a real data set. (c) 2004 Elsevier Inc. All rights reserved.