Robustness and inference in nonparametric partial frontier modeling

A major aim in recent nonparametric frontier modeling is to estimate a partial frontier well inside the sample of production units but near the optimal boundary. Two concepts of partial boundaries of the production set have been proposed: an expected maximum output frontier of order m = 1, 2, ... and a conditional quantile-type frontier of order alpha is an element of ]0, 1]. In this paper, we answer the important question of how the two families are linked. For each m, we specify the order alpha for which both partial production frontiers can be compared. We show that even one perturbation in data is sufficient for breakdown of the nonparametric order-m frontiers, whereas the global robustness of the order-alpha frontiers attains a higher breakdown value. Nevertheless, once the alpha frontiers break down, they become less resistant to outliers than the order-m frontiers. Moreover, the m frontiers have the advantage to be statistically more efficient. Based on these findings, we suggest a methodology for identifying outlying data points. We establish some asymptotic results, contributing to important gaps in the literature. The theoretical findings are illustrated via simulations and real data. (C) 2010 Elsevier B.V. All rights reserved.