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 and a conditional quantile-type frontier of order . In this paper, we answer the important question of how the two families are linked. For each , we specify the order 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- frontiers, whereas the global robustness of the order- frontiers attains a higher breakdown value. Nevertheless, once the -frontiers break down, they become less resistant to outliers than the order- frontiers. Moreover, the -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.