On estimation of monotone and concave frontier functions

The productivity of a firm is analyzed in terms of the maximal level of output that can be achieved for a given combination of inputs. This is made possible by estimating the monotone and concave frontier functions using an improved bias-corrected estimator. The bias-corrected estimator is derived by obtaining the asymptotic distribution of the data envelopment analysis estimator and its finite-sample performance is assessed in a simulation study. The proposed estimator is based on consistent estimation of the density function and the second derivative of the production frontier to define the economic efficiency of a firm.
1. INTRODUCTION Suppose that ([X.sub.1], [Y.sub.1]), ..., ([X.sub.n], [Y.sub.n]) are iid with a density f in [R.sup.2]. The support of f is assumed to be of the form [Psi] = [...]