Stochastic Nonparametric Envelopment of Data: Cross-sectional frontier estimation subject to shape constraints

The field of production frontier estimation is divided between the parametric Stochastic Frontier Analysis (SFA) and the deterministic, nonparametric Data Envelopment Analysis (DEA). This paper explores an amalgam of DEA and SFA that melds a nonparametric frontier with a stochastic composite error. Our model imposes the standard SFA assumptions for the inefficiency and noise terms. The frontier is estimated nonparametrically, imposing monotonicity and convexity as in DEA. For estimation, we propose two alternative methods based on shape constrained nonparametric least squares. The performance of the proposed estimation techniques is examined using Monte Carlo simulations and an illustrative application.