Frontier estimation using kernel smoothing estimators with data transformation

In economics, a production frontier function is a graph that shows the maximum output of production units such as firms, industries, or economies, as a function of their inputs. Practically, estimating production frontiers often requires imposition of constraints such as monotonicity or monotone concavity. However, few constrained estimators of production frontier have been proposed in the literature. They are based on simple envelopment techniques which often suffer from lack of precision and smoothness. Motivated by this observation, we propose a smooth constrained nonparametric frontier estimator respecting constraints by considering kernel smoothing estimators from a transformed data. It is particularly appealing to practitioners who would like to use smooth estimates that, in addition, satisfy theoretical axioms of production. The utility of this method is illustrated through application to one real dataset and simulation evidences are also presented to show its superiority over the most known methods.