This paper focuses on nonparametric efficiency analysis based on robust estimation of partial frontiers in a complete multivariate setup (multiple inputs and multiple outputs). It introduces α-quantile efficiency scores. A nonparametric estimator is proposed achieving strong consistency and asymptotic normality. Then if α increases to one as a function of the sample size we recover the properties of the FDH estimator. But our estimator is more robust to the perturbations in data, since it attains a finite gross-error sensitivity. Environmental variables can be introduced to evaluate efficiencies and a consistent estimator is proposed. Numerical examples illustrate the usefulness of the approach.
Daouia, A., & Simar, L. (2007). Nonparametric efficiency analysis: a multivariate conditional quantile approach. Journal of Econometrics, 140(2), 375-400. https://doi.org/10.1016/j.jeconom.2006.07.002 (Original work published 2007)