In frontier analysis, most of the nonparametric approaches (free
disposal hull [FDH], data envelopment analysis [DEA])
are based on envelopment ideas, and their statistical theory is now mostly
available. However, by construction, they are very sensitive to outliers.
Recently, a robust nonparametric estimator has been suggested by Cazals,
Florens, and Simar (2002, Journal of
Econometrics 1, 1–25). In place of estimating the full
frontier, they propose rather to estimate an expected frontier of order
m. Similarly, we construct a new nonparametric estimator of the
efficient frontier. It is based on conditional quantiles of an appropriate
distribution associated with the production process. We show how these
quantiles are interesting in efficiency analysis. We provide the
statistical theory of the obtained estimators. We illustrate with some
simulated examples and a frontier analysis of French post offices, showing
the advantage of our estimators compared with the estimators of the
expected maximal output frontiers of order m.We thank J.P. Florens for helpful discussions and C. Cazals
for providing the post office data set. We also are very grateful to the
referees for useful suggestions.