Recently, in an attempt to produce robust production frontier estimators, Aragon et al. [2005, Nonparametric frontier estimation: a conditional quantile-based approach. Econometric Theory 21, 358-389] and Martins-Filho and Yao [2008, A smooth nonparametric conditional quantile frontier estimator. Journal of Econometrics 143, 317-333] considered the estimation of nonparametric α- frontier models...