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 α ∈ ] 0 , 1 ] . In this paper, we answer the important question of how the two families are linked. For each m , we specify the order α 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- α frontiers attains a higher breakdown value. Nevertheless, once the α 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.