Parametric approximations of nonparametric frontiers

The maximal achievable level of output for a given level of inputs defines the production frontier that can serve as benchmark to evaluate individual firm efficiencies. Nonparametric envelopment estimators (free disposal hull, data envelopment analysis) have been mostly used because they rely on very few assumptions, whereas parametric forms for the frontier allow for richer economic interpretation. Most of the parametric approaches rely on standard regression fitting the shape of the center of the cloud of points. In this paper, we investigated a new approach, which captures the shape of the cloud points near its boundary. It offers parametric approximations of nonparametric frontiers. We provide the statistical theory (asymptotic). Some simulated examples show the advantages of our method compared with the usual regression-type estimators.