Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach

Abstract

In frontier analysis, most of the nonparametric approaches (FDH,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). 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.

X-efficiency and economies of scale in pension fund administration and investment

“…To deal with this problem, partial frontier approaches have been developed. Partial frontier approaches, such as Order−α (Aragon et al, 2005) and Order−m (Cazals et al, 2002) efficiency, allow for superefficient observations, which are below the cost frontier. Superefficient observations can represent random shocks (luck) or measurement noise, but do not necessarily represent sustainable best practices.…”

Costs, revenues and performance in Spanish banking: a comparative analysis of pre- and early crisis years

“…However, in the last ten years the proposals in the nonparametric field have outnumbered those in parametric field. These proposals include the order-m (Cazals et al, 2002) and order-α (Aragon et al, 2005;Daouia and Simar, 2007) estimators, which are more robust to extreme values than either DEA or FDH (Free Disposable Hull). Although these methods are gaining wider acceptance, some critiques have also been put forward (Krüger, 2012).…”

On the informativeness of persistence for evaluating mutual fund performance using partial frontiers

“…The order-m ideas can easily be adapted to order-α quantile type-frontiers. The underpinnings of order-α were initially developed for the univariate case by Aragon et al (2005) and extended to the multivariate setting by Daouia and Simar (2007), and are similar to those of quantile regression (Koenker, 2001).…”