-European Journal of Operational Research 231 (2013) 481–491；
Isotonic nonparametric least squares (INLS) is a regression method for estimating a monotonic function
by fitting a step function to data. In the literature of frontier estimation, the free disposal hull (FDH)
method is similarly based on the minimal assumption of monotonicity. In this paper, we link these
two separately developed nonparametric methods by showing that FDH is a sign-constrained variant
of INLS. We also discuss the connections to related methods such as data envelopment analysis (DEA)
and convex nonparametric least squares (CNLS). Further, we examine alternative ways of applying isotonic
regression to frontier estimation, analogous to corrected and modified ordinary least squares
(COLS/MOLS) methods known in the parametric stream of frontier literature. We find that INLS is a useful
extension to the toolbox of frontier estimation both in the deterministic and stochastic settings. In the
absence of noise, the corrected INLS (CINLS) has a higher discriminating power than FDH. In the case
of noisy data, we propose to apply the method of non-convex stochastic envelopment of data (nonconvex
StoNED), which disentangles inefficiency from noise based on the skewness of the INLS residuals.
The proposed methods are illustrated by means of simulated examples.